[Music] hello everyone welcome back to deb tv i am ms dj and i'm going to be your study body for today with a joyful heart and an empowered mind and spirit learn along with me and let's be mad kaling so now bring out your pen and your self-learning module as we demystify the mathy magical world of sets [Music] [Applause] [Music] in today's episode we are going to learn a whole bunch of things about sets but first let us answer these pre-assessment questions you have three seconds to answer each question timer one which of the following is a well-defined set a a set of beautiful sceneries b a set of good basketball players c a set of philippine presidents d a set of successful leaders timer [Music] the correct answer is letter c a set of philippine precedents second question which of the following is a symbol of a null or an empty set timer the correct answer is letter d that is the symbol for a null or an empty set third question which symbol is used to indicate the intersection of sets timer good job the correct answer is letter a this is the symbol to indicate the intersection of sets fourth question the following is a subset of set r which contains the letters n e and w except a the set containing n e w b the set containing e c the set containing 0 d the set containing e and w timer so what is your answer perfect the correct answer is letter c for our fifth and last p assessment question which of the following set has the cardinality equals to 5 is it a set a is the set of counting numbers less than 5 b set b is the set of letters in the word racer c set c is the set of positive multiples of five or d set d is the names of the fingers timer the correct answer here is letter d since this set has five elements which are used to name the different fingers in either hands we will explore more on cardinality of sets later triangles have been regarded as a symbol of the trinitarian belief by christians while a filipino song entitled tatsulok originally performed by booklot and popularized by bamboo has politically used it to symbolize inequalities in our society now how do we describe a triangle first it has three sides it has three interior angles whose sum is always equal to 180 degrees and its shape is recognizable as one with the base and opposite it is a vertex of the triangle which for certain types of triangle is referred to as its index in this collection which does not belong to the group correct the artworn out is the four-sided figure placed on the fourth spot now what is the term used for the collection of objects or quantities in mathematics a well-defined group or collection of objects that share the same characteristics is called set the objects found in the set are called elements a set can be using capital letters from a to z and we use braces to group the elements of the set separated by commas if a set contains many elements we often use t dots called ellipses note that in listing the elements in the set each distinct element is listed once and the order of the element does not matter this means that a set can be written in different order but shall pertain to the same set like in set j which are the letters in the word idol this set is the same as set j which contains l o d i to understand what makes sets well defined let me give you some examples first set m is the set containing primary colors and we read this as set m contains the elements red yellow and blue second set s is the set of letters in the word sipnayan set s contains the element s i p n a and y and set e is the set of all even numbers thus set e contains the elements 2 4 6 8 and so on here on the other hand are not well-defined sets the set of famous dancers the set of honest people the set of punctual students in your class why because our view of fame honesty and punctuality may be subjective so we could come up with different lists of famous or honest or punctual people as my way to confirm that you have learned something from our discussion let us answer the following questions match the descriptions in column a with the word or words being described in column b write your answer in the space provided number one these are the objects contained in the set the correct answer is letter e elements are the objects contained in the set number two a well-defined group or collection of objects that share common characteristics that is letter b set is a well-defined loop or collection of objects that share common characteristics number three it is represented by three dots which is used to indicate that a set has many or infinite elements the correct answer is letter c ellipsis ellipsis is represented by 3 dots which is used to indicate that a set has many or infinite elements number four a symbol used to group the elements of a set the correct answer is letter d the brace symbol is used to group the elements of a cell [Music] now you shall go deeper into sets and relationships in sets but first let us add the following words to our vocabulary to be able to express ourselves concisely and proficiently in the language of sets the words are subset universal set empty set cardinal number of sets and disjoint sets let me give you a complete example the given is set a contains the number 0 1 2 3 4 5 6 7 8 9 10. from this we need to find one the set of odd numbers two the set of all factors of ten three the set of multiples of four and four the set of negative integers let's say in this case a is the universal set if you form another set from set a say set o consisting only of the set of odd numbers from 1 to 10 then we can say that set o is a subset of set a please take note that the set is a subset of another if each of the element of the former is an element of the latter again using the same set a let's say we have two more sets that are subsets of set a this are set o and set b we see here that sepsis and set b are disjoint sets because they do not have elements in common how about number four in the given problem can we draw out negative integers from our given set set a [Music] okay none the empty set or null set is denoted by a circle slashed with a slant line in the middle did you know that you can insert this symbol in microsoft word by typing 2205 alt x that's awesome right and lastly the cardinal number of a finite set a is the unique counting number n such that the elements of set a have one-to-one correspondence with the elements of the set one two three ellipses up to n for example set a contains a e i o u this only means that the cardinality of set a here is five therefore if we were to answer number five in our p assessment earlier which of the following set has the cardinality equals to five is set a set a is the set of counting numbers less than 5 set b is the set of letters in the word racer set c is the set of positive multiples of five or d set b is the set of names of the fingers what is the correct answer yes very good d is the correct answer unlike the other sets the cardinality of set d is five set a has four elements that is set a contains the elements one two three four set b has also four elements because although razer is a five letter word the element r must only be written once thus set b has elements r a c e on the other hand the third set set c has infinite elements thus its cardinality is not also equal to 5. option b has a total of 5 elements namely thumb index finger middle finger three finger and pinky to completely grasp this concept let us have more examples in this activity we need to find the cardinality of the following sets set r is the set of letter in the word difficulty to solve it you need to list down all the letters in the word difficulty regardless if the letter repeats set r contains the elements d i f c u l t and y therefore the answer is n of r is equal to 8 set m is the set of odd numbers between 1 and 3. 1 and 3 are consecutive odd numbers and there are no more odd numbers between them so set m has no elements and the answer is n of m is equal to zero [Music] set k is the set of counting numbers less than five to solve you need to list down all the numbers less than five so k contains the elements one two three four therefore the answer is n of k is equal to four alfred whitehead once said to see what is general in what is particular and what is permanent in what is transitory is the aim of scientific thought as a philosopher mathematician he believes your knowledge of the particular facts of the world around you is gained from your very own sensations we use sets and its related concepts in other fields at this point we will answer the following questions to evaluate what you have learned about sets are you ready citrix it in a minute can you try answering the following for just a minute select the letter that corresponds to the correct answer timer first question which of the following is a well-defined set a a set of good writers b a set of factors of ten c a set of fashionable actresses in our country number two which of the following is a symbol of null set look at your screen for the options number three michelle listed the set of letters of survival as shown in your screen what is wrong with the set a it uses commas b it uses braces c some objects in the list are not listed once or d a lowercase letter is used to represent the name of the set question number four given the set of letters in the word love what is the cardinality of the set a 11 b a c 6 or d four [Music] let's check your test be precise and truthful okay the correct answers are number one b a set of factors of ten is the well-defined set since as we used in one of our example it has shared characteristics its elements are 1 2 5 and 10. number two the correct answer is d a symbol for null set is a circle slashed with a slant line in the middle number 3 c is the set that is wrong because some objects in the list are not listed once [Music] for number 4 the correct answer is d 4 is the cardinality of the set of letters in the word [Music] love you should congratulate yourself if you have a good grasp of sex and its related concepts i am delighted to be with you today we will learn more about sets in our next episode and you will be introduced to set operations and venn diagrams again this is miss bj i wish you all a blessed day and i hope to see you again here in mad deluge tv [Music] you