In this lecture, we are going to talk about the three most important fundamental aspects of propositional logic. That is propositional logic itself, propositional variables, and compound propositions. Now let's try to understand what is propositional logic.
Propositional logic is an area of logic that studies ways of joining and or modifying prepositions to form more complicated looking prepositions. In prepositional logic, we find out the ways of joining and or modifying prepositions to form more complicated looking prepositions. It also studies the relationships among them as well as the properties that are derived from these combined or altered prepositions. Now let's try to understand what does this definition really mean. Let's consider this statement.
Adam is good in playing football. Let's consider one more statement. Adam is good in playing football and this time he is representing his college at national level. Not only Adam is good in playing football, but this time he is also representing his college at national level.
Here I have rewritten this statement. If you observe carefully, in this statement we are trying to combine two propositions together. Right? This is the first proposition, Adam is good in playing football.
And this is the second proposition, this time he is representing his college at national level. We are trying to combine these two propositions together with the help of one logical connective called AND. And this is what propositional logic deals with.
As we know it studies the ways of joining propositions to form more complicated looking propositions. Here also we are combining two two prepositions together and form up a more complicated looking preposition. Okay. Now let's consider some more examples. Let's consider the statement I enjoy watching television.
Now let's consider this statement. It is not the case that I enjoy watching television. What is the difference between these two statements?
This particular statement is the negation of this statement. Isn't that so? Here we are trying to modify the statement using negation. And this is also what we learned in the definition of propositional logic.
Not only we are trying to combine two or more propositions together, but we also modify propositions in propositional logic. Let me tell you one important fact. Propositional logic is sometimes called as Sentential logic or statement logic.
And we know this already, why propositional logic is also called as sentential logic or statement logic. Because propositional logic is dealing with statements like these. It tries to find out the ways of modifying or joining the propositions together so that we would be able to form even more complicated propositions. Right?
Now let's try to understand why do we need compound propositions. What is the need of creating those complicated looking propositions also called as compound propositions? Because most of the mathematical statements are constructed by combining one or more than one propositions. Isn't that so? That is the reason why we are considering compound propositions.
Finally, we need to deal with mathematical statements and most of the mathematical statements are formed by combining Do or more propositions. As simple as that. After talking about propositional logic and how do we able to combine propositions and modify propositions, now we are going to study what is propositional variable.
Let me ask you one question. Which one of the following is convenient to express? Adam is good in playing football. And this time he is representing his college at national level.
Is this one convenient to write? Or is this one is convenient to write? Suppose I represent this statement Adam is good in playing football by P and this statement, this time he is representing his college at national level by Q.
Instead of writing this statement we can also write P and Q. Isn't that so? Because P is representing the first preposition and Q is representing the second preposition.
And we are combining these two propositions using this AND operator. This is called AND operator in propositional logic. This is equivalent to P and Q.
Okay. Now it is not very difficult to understand why do we need propositional variables. Propositional variables helps us to reduce the burden of writing these long long statements.
Instead of writing these long long statements, we would be able to represent them in this form. Which is much convenient to write as well as much convenient to deal with. Now let's talk about the definition of propositional variables. Variables that are used to represent propositions are called propositional variables.
Simple. These are the variables which are used to represent the propositions. And then, it is much convenient to combine these two propositions using certain operators that are available in propositional logic. We will talk about this operator as well as more operators available in propositional logic. In the subsequent lectures, right now it is sufficient to know that we would be able to represent propositions using propositional variables.
And finally, we would be able to combine them using these operators. Okay friends, this is it for now. Thank you for watching this lecture.