[Music] hi this is Matt it LSAT lab and today's lesson is on must be true questions in the logical reasoning section but 4% of all questions in logical reasoning are must be true questions so they're not a very common question type but they're a really important one because they set a good foundation for how to think about logical reasoning and the complexity involved with these questions typically tends to make them harder than normal so it's a it's a harder question type for a lot of people in this lesson we're gonna look at how to spot a must be true question an example question that contains conditional logic an example question that contains comparison an example question that contains causation and then we'll finish by looking at the trap answer patterns that you need to know about in order to be able to get down to the right answer take a look at this question stem if the statements above are true which one of the following must also be true well the words must be true are contained within the questions - this one's pretty obvious there's asking you to find what must be the case in this one it asks which one of the following can be logically inferred from the statements above inferred is the same on the LSAT as must be true so if they if you see them asking for what can be inferred they're asking you for what you know to be true which one the following can be properly concluded from information given so something that it can be properly concluded is the same as something that can be properly inferred both of which are things that must be true in this one we're asked to find a consequence of the view above well that means what follows from that view what do we know to be true this one says if the statements in the passage are true each of the following must be true except this is asking us to find what must be the case but it says that four of answer choices are things that must be true the one that does not have to be true the one that could be false this is gonna be the right answer so now that we know how to find it must be true question let's talk about the process that you want to use when working on one well the first step is to find the related statements so there will be multiple statements within the stimulus and they should be talking about something it's in common they typically will link together through that relationship so if there if there's a term that's connecting two different statements together it's through that term that the inference is gonna be made right so we want to look out for terms repeated across the sentences we want to think about the kind of reasoning that those sentences contain so are we working through an if-then relationship like if a then B if B then C or are we looking at a comparative relationship where one thing is bigger than or faster they had something else we want to use our understanding of the connected term and the kind of relationships contained within those statements in order to better anticipate what an answer might sound like what what could those statements imply or what do those statements imply that we can then use to kind of pre phrase what the answer would sound like and then we want to work through the answer choices generally working from wrong to right there might be times when you're on an easier question and you'll know exactly what you want to be looking for ahead of time and you'll find it you'll pick it you move on that's fine but you may also encounter many situations where you can get rid of a couple of their choices rather quickly but to dive deep and to really figure out what each of the remaining choices are saying you need to spend a little bit more time right so in those cases you'll probably want to work from wrong to right where you're gonna use trap answer patterns to help you make eliminations so you can get to the right answer so the first example question we're gonna look at in this lesson is on conditional logic and conditional logic is the major player when it comes to reasoning structures in must be true questions 75% of must be true questions contain if-then conditional logic so if you have two if-then statements and they contain a common term you might be able to connect them together using the transitive property in order to get an inference something that must be true given those two relationships well if we know if a then B and if B then C what can we infer well using the transitive property we can link through the be in a infer that if a is true then C is true this this particular structure where we have two premises two pieces of evidence that are if-then relationships and a conclusion that is also an if-then relationship that follows from them there's a SAN for this particular structure it's called a syllogism and it's one of the most common structures that you're gonna see on the LSAT this announced your turn let's try example here given these statements which of the following must be true hit pause see if you can find the right answer and then come back and we'll review together all right welcome back so let's start with and trace a and see if we can figure out whether that is something that we can prove if K then P well what we're gonna do is look at the statements that involve a K and a P and see if we have either the K on the left of one of the relationships or the P on the right of one of the relationships we're trying to imply if K then P or trying to prove if k then P we're gonna need to see a K on the left of a premise and a P on the right of a premise when we start with you know the first premise we actually know if cade an M and if we look at the second premise if P then not M we can take the contrapositive of that and we know if M then not P contrapositive is when you reverse and negate a conditional relationship so now we have if K then M and if M then not P so what can we infer we can infer if K then not P but that's different than if K and then P in fact a is something that must be false is not something that must be true we look at n cos B if P then not L so what we're gonna look for is either a P on the left of a premise or not L on the right of a premise we have a p on the left in the second premise so we know if P then not M now for in terms of L we have an L on the right in the third premise and we have an L on the left of the first premise well and L on the right isn't going to allow us to infer not L it would allow us to infer L but that's not the same and we can't really get to it anyways because we're right now at not M but if we take the contrapositive of the first premise if we know if not m then we know not L and not Kay we don't necessarily care about the part with Kay but we know not L so if not M then not L and so between the second premise and the first premise we are able to infer if P then not L that must be true that's the right answer now if that's choice C if M then L what we want to do is either see if there's an M on the left or an L that's on the right we have an M on the right in the first premise we have an L on the right in the third premise so let's go ahead and add the third premise in and figure out if we can get an M on the left somehow if we take the contrapositive of the first premise we get if not M then not K and if not K we know from the third premise that not that L is implied so we can get to if not M then L but we can't quite get to if M then L can get close but not quite and so C is not something that must be true in this wrong so now let's take this idea of working with conditional relationships and linking them together in order to derive inferences and to apply this to a real LSAT question so go ahead and give this question a try it on your own and see if you can find answer the choice that you like and when you're ready to review this together hit play alright welcome back so what are we told here if the price it pays for coffee beans continues to increase the coffee shop will have to increase its prices the word if gives us a conditional relationship so if the price paid for beans goes up then coffee shop is going to have to increase their prices and then we're told in that case either the coffee shop will begin to selling non coffee products or its coffee sales will decrease so if they in that case is referring to if they are increasing their prices the word that is reflexive referring back to the previous term and then we have an or statement on the right side of this relationship either they're gonna have to start selling non coffee products or their sales are going to decrease next we're told lets selling non coffee products will decrease the coffee shop overall profitability so if they sell non coffee products it's gonna decrease the profits and finally we're told moreover the coffee shop can avoided decrease in overall profitability only if it's coffee sales do not decrease only if tells us that it's coffee sales not decreasing is a necessary condition and the coffee shop can avoid a decrease in overall profitability is a sufficient condition now if we take the contrapositive of that relationship we end up with if the sales decrease then the decreases that decreases profits and so now we have the four statements from the stimulus that we can look for related terms terms that connect together we know we're working within conditional logic but what are the connections that can be drawn from these statements so if the price paid for beans goes up then they're gonna have to increase their prices and if they increase their prices that means that they're gonna either start selling non coffee products or their sales are going to decrease notice if they sell non coffee products or their sales decrease either one of those implies that they're going to have decrease in profits and so we can infer from these relationships that if the price paid for beans goes up then they're gonna have a decrease in profits no matter what and so that would be my pre phrase of my best guess at what the right answer is going to say introduced a says if the coffee shops overall profitability decreases the price it pays for coffee beans will have continued to increase the if tells us what's the sufficient condition that overall profitability has decreased so we have a decrease in profits and it tells us that the price it pays for coffee beans is the necessary condition so the price paid for beans goes up answer choice a has the right terms of our pre phrase but it has the the direction of the relationship backwards and so entities a represents the most frequently chosen trap answer pattern on must be true questions which is that of a reversal answer choice B says if the coffee shops overall profitability decreases either will have begun selling non coffee products whereas coffee sales will have decreased the word if tells us tells us how to organize this relationship so if you have a decrease in profits then either we're selling non coffee products or this say are going to decrease so we have these terms connected in relationships but the relationships imply the reverse so again this is another reversal tempting but wrong answer choice answer to AC says the coffeeshops overall profitability will decrease if the price it pays for coffee beans continues to increase the word if is buried in the middle of the statement there but it's really important because it tells us that the price paid going up is the sufficient condition and the overall profitability going down is the necessary condition and so this actually matches our pre phrase so this looks like a strong contender let's hold on to it if you're looking at choice D says the price it pays for coffee beans cannot decrease without the coffee shops overall profitability also decreasing well if we want to put this into an if-then relationship we are gonna use the word without without is going to introduce the necessary condition right so the profitability decreasing is the necessary condition but the word without is special and then it's gonna negate the sufficient condition so the price it pays for coffee beans cannot decrease when we negate that it says if the price that pays for coffee beans does decrease well if the price it pays decreases then we're gonna have a decrease in profits well we know that if the price it paid for beans increases we would have a decrease in profits so that's choice D is fairly close but it's got the wrong sufficient condition it's it's an unsupported relationship we know that if the price paid goes up that they're gonna have a decrease in profits we don't know that if the price paid goes down they're gonna have a decrease in profits that may be true but there's no way to prove it with these statements the answer choice E says that either the price it pays for coffee beans will continue to increase or the coffee shops coffee sales will increase we can write that as an or statement but we can also interpret it into an if-then relationship we can say if one of those things doesn't happen then the other must happen so we could write it as if the price it paid for beans does not go up then the sales have to increase and if we compare that against the statements in the statements that we have we know that if the price paid for means goes up that sales are gonna decrease this looks like a negation of the relationship that we can get close to proving so it's another common trap reversals and negations are gonna be what they use in order to get an answer trace to sound very very similar to what you're looking for and yet have a say something a little bit different and so aunt Tracy is the right answer so now let's look at an example that involves comparison 19% of must be true questions involve comparative reasoning an example of what compared of reasoning looks like is we might have let's say city a is more populous than city B we got more people in city a density B and they might also tell us that city a is geographically smaller than city B so it takes up less space if we know those two things are true what else do we know we would know that the density of city a is much greater than the density of city B and so that's the kind of relationship that we're looking to get from a comparative reasoning structure typically comparisons take one two forms on the LSAT either they're comparing two different things at a point in time like in this example here or they compare one thing over two different points in time let's say they were comparing City a today versus City a ten years ago that would be another way in which they could get it similar but somewhat different sounding comparison and the interplay between those two is very interesting because if you know that you can infer a comparison between two different things at a point in time they may give you an answer choice that compares a thing at two different points in time that might sound very tempting but would be still wrong so go ahead and try this example on your own when you found an answer that you like it play again and we'll work it through together all right welcome back so what are we told in this question well we're told that no headache pill stops paying more quickly than two naxal so that means that the naxal is quite possibly the fastest etic pain pill out there but you know by saying that no headache pain pill stops paying more quickly that doesn't exactly tell us how fast an axle is or how fast the leading competitors are there's a range of possibilities that would satisfy that that idea but we know that there are no competitors that are faster than an axle so maybe Dan axle cures headache pain in about 20 minutes whereas the competitor might take 2530 but what's what's deceptive about that claim is that if the leading competitor stops pain in 20 minutes exactly then it's not lying to say that no headache pill stops paying more quickly than an axle this leaves open the possibility that the competitors are also curing headache pain in about 20 minutes or 25 minutes or 30 minutes 35 minutes anything that's at least as long as Dan axle that's all we care about okay so it's more like a weak inequality rather than a strict inequality this statement is not saying that Dan axle cures headache pain faster than its leading competitors instead what it is saying is that nobody is faster than Dan axle which leaves open the possibility that they all Kier heading pain at the same exact speed so now let's look at the choices and trace a says that Evelyn's headache pain will be relieved but James will not well the idea that James is not going to be relieved but it does say in the stimulus that all headache pills can stop your headache so if anything in straights a is probably contradicted by the statements and stress be Ellen's headache pain will be relieved more quickly than James this would be a very very tempting answer choice in fact most people probably pick this answer choice because it sounds like the statement is implying that the Naxals the fastest but that's not necessarily true it could be the case that they all cure headache pain in exactly the same amount of time and to say it's so to say that Evelyn's headache pain will be relieved more quickly than Jaynes it's simply too strong there's more than what we know and that makes it wrong it's Joyce C says Evelyn's headache will be relieved at least as quickly as Jaynes know what they're hoping for is that you were going to read answer to as B fall in love with it and move on to the next question without reading C D or E if you at least even if you love B you should have a chance to correct your error by by by internalizing what C is saying well if Evelyn's headache pain will if you like the idea that Evelyn's had a pain will be relieved more quickly than James you should also like the fact that Evelyn's headache will be relieved at least as quickly as James the difference being is that C is a little bit weaker way of saying the same thing and so actually C looks like a really good contender answer choice D says that Jane's headache pain will be relieved at the same time as Evelyn's now if you weren't aware of the difference between an traces B and C the fact that answer is D is pointing out that things can happen at the same time is your clue about the difference between them B is suggesting more quickly C is saying at least as quickly D is saying hey there could be a tie and that tied should help you understand the difference between entities B and C it should also help you understand why D is wrong right that that relationship is unsupported answer Tracy says that Jane will be taking two naxal for relief from headache pain well we don't know that we don't know that Jane will be taking the neck so if anything we know that all headache pain pills can stop the pain so that's actually an unsupported relationship and so answer is C is correct let's look at another example this one involving causation now causation is rare one must be two questions it can still occur and and so here's an example question in which we find causal reasoning at play couldn't give it this one try see if we can find an answer that you like and then when you're ready to review together hit play again alright welcome back this question is asking for what can be properly inferred from the information above so inferred sounds like must be true and we're given a series of statements the first statement saying that the calm shallow waters of coastal estuaries are easily polluted by a nutrient-rich sewage so that's the saying that the sewage causes pollution the second statement says that when estuary waters become over nutria fide as a result algae Pro proliferate the words as a result are critical there because they're helping as I defy the causal reasoning the pollution causes algae the neck statement says that the button algae in turns sometimes provide a rich food source for microorganisms that are toxic to fish so the algae cause toxic organisms and the last statement said thereby killing most of the fish in the estuary so the toxic organisms kill the fish so this example presents a causal chain where the sewage causes pollution the pollution causes algae the algae causes toxic organisms and the toxic organisms caused a die-off of fish so this causal chain allows us to make inferences we can move along the causal chain in a forward direction the same way we can with conditional relationships now we've notated a little bit differently because we want to be clear about the difference between an if-then relationship in a causal relationship and if then relationship is a correlation there's a perfect correlation in one direction between two events whereas a causal relationship is a is a correlation between two events but it implies that one thing is the thing that creates the next right there's a deeper form of a relationship than a simple conditional relationship now if you look at the choices in choice a says that fish in an estuary that has been polluted by sewage are generally more likely to die from pollution than are fish in an estuary that has been polluted in some other way so now this is comparing an estuary that's been polluted by sewage and another one that's been polluted in some other way in the relationship or the the likelihood that the fish are to die well we don't know anything about estuaries where they've been polluted in some other way this is simply either out of scope or it's an unsupported relationship the more likely to die creates an unsupported relationship and polluted in some other way creates a topic a term that is out of scope and strays B says in estuary waters that contain abundant algae microorganisms that are toxic to fish reproduce more quickly than other types of microorganisms notice the words more quickly then this is building a comparative relationship we were dealing with a causal structure B is presenting a comparator relationship that's simply an unsupported relationship answer IC nutrients and other components of which do not harm fish in coastal estuaries in any way other than through the resulting proliferation of toxic microorganisms well notice that they talk about ways in which ways other than through the resulting proliferation of non-toxic microorganisms similar to answer choice a where it talked about estuaries that were uploaded in some other way in answer to a see when they talk about other than through the resulting proliferation of toxic microorganism is simply out of scope we don't know anything about that answer twice D says algae will not proliferate in coastal estuaries that are not polluted by a nutrient-rich sewage so this is a relationship between two of the terms the algae proliferating and not being polluted by nutrient-rich sewage so this is basically negating the relationship between sewage to pollution pollution to algae so if we don't have sewage then we're not going to get the pollution if we don't get the pollution and we're not gonna get the algae negating that relationship doesn't work for words we cannot establish a relationship moves forwards through a causal chain saying that if we don't have the first we're not gonna have the latter so that's a negation in terms of the relationship that only leaves us for the answer to AC hopefully this turns out to be the right answer over nutria fiying estuary waters by sewage can result in the death of most of the fish in the estuary well over nutria fighting estuary waters absolutely that's the sewage can resulting gives us a causal relationship and the death of most of the fish in the estuary the only thing I might check is whether or not we're talking about most of the fish if we go back into the stimulus thereby killing most of the fish in the estuary it matches so as Chris II is the right answer all right so let's now talk about the different trap answer patterns that we can face on must be true questions we saw several of them in those three examples but let's just lay this out in terms of frequency so in terms of scope we have entities that are either out of scope or mere speculation about some situation that we are not told anything about trap answers relating to logic are those that are unsupported relationships either they're building the wrong type they're building a relationship and that the wrong type of reasoning or they're just randomly grabbing two terms from the stimulus and connecting them in a way that can't be supported by the statements ancient races that are the opposite of what you're looking for so instead of looking for what must be true in each race that represent something that must be false can often be really tempting because it's it has the right terms it just has the the signage of one of them wrong so entrances that contradict the the statements can sometimes be very tempting introduces that reverse or negate conditionals or causal chains can be very tempting and then answer choices that lead or lend support to one of the statements being true we're looking for what follows from the statements so an instance that makes one of them more likely to be the case doesn't actually follow from them but they do seem connected in some way so entries that are supporting one of the statements in the stimulus in terms of degree and traces that are too strong will be the tempting but wrong in choice so really look out for introduces that are just presenting strength it's not that every strong answer is wrong it's just that answer choices can get into into trouble for being too strong but they cannot get into trouble for being too weak so in summary you spot a must be true question with language such as must be true or inferred or follows logically can be concluded these are terms that will help you in the question stem itself identify this particular question type so the reasoning structure you really want to be on the lookout for when you're working on must be two questions is conditional logic although comparison and causation also do play minor roles and the trap answer patterns do you really want to be paying attention to are those that are building relationships either in the wrong type of reasoning or connecting the wrong terms and traces that are simply stronger than when you know those that reverse or negate an implied relationship or those that contradict the statements so that's it for today's lesson on must be true questions I invite you to check out some of these other videos or visit us today at LSAT lab calm