Learn about Related Conditional Statement In this lesson, let’s learn about related conditionals. And related conditionals are converse, inverse and contrapositive statements and they are all formed from the conditional statement. Let me explain what we mean. So, if we see a conditional statement which says, if p then q, we write it as p and arrow towards q. So, this is the conditional statement. The converse of the statement basely allows us to swap the two values which is if q then p. The inverse is if not p, then not q. This is the symbol for not. If p is not true then q is not true. And the contrapositive is if not q, then not p. Let me repeat the four things that we talked about. The conditional statements is if p then q. The converser of it is if q then p. Just flip these two around. The inverse of the conditional is, if not p then not q. This curvy line is the symbol for not or the inverse of it and then if not q, then not p is called the contrapositive. So, let’s use this example and write each one of these. This is the conditional. So here, the hypothesis is animal is a cat and conclusion is it has four paws. So, this is the conditional. Now, let’s write the converse. The converse is we swap the hypothesis and the conclusion. So, if it has four paws then an animal is a cat. Let’s do this. Is this actually true? If the animal is a cat, does it have four paws? Every cat has four paws so this is true. But if we look at the converse, if an animal has four paws then is the animal a cat? Well, a lion has four paws but it is not a cat which means the converse is not true. I found the counter example of in a lion which has four paws but it’s not a cat or I could even say dog, right? A dog is never a cat. Now, let’s look at the third one which is the inverse. The inverse is if not p, then not q which means if the animal is instead of a cat we say not a cat. Then, it is does not have four paws. Is this true? Well, if animal is not a cat, so let’s pick an animal that’s not a cat. Let’s say dog. Then it cannot have four paws. Well, a dog has four paws so this is again not true. You’ll notice what we did is we just said if the original hypothesis is not true, then the original conclusion cannot be true. So, this is not true. The inverse of the statement is not true. Let’s do the last one which is the contrapositive. Contrapositive is if not q then not p, which means if it does not have four paws. Then animal is not a cat. Let’s see if this true. If an animal does not have four paws, so let’s take an animal like a chicken that only has two paws, two legs then it’s not a cat. So, for an animal to be, it must have four paws, so this is true. So, when we look at creating the conditional table, what are we given? So, we are given that the condition is true. The contrapositive is true, but the converse and inverse are false. This is called the Law of Conditionals. If the condition is true then chances are the contrapositive is also true.