 Conditional statements are statements made in logic these will be the reason we're talking about them is because we will be using them in proofs in upcoming chapters. There are two parts to a conditional statement the hypothesis which just like in science is the maybe I think I believe that if I water the plants they'll grow taller and let me check it out now so this is the perhaps if you're 16 the conclusion would be then it is legal for you to have a driver's license so in a conditional statement the hypothesis is the if portion of the statement the conclusion is the then portion of the statement there are there's a way to represent conditional statements symbolically as well if P then Q where P is the hypothesis Q is the conclusion if P then Q and the logic symbol for if then is this arrow symbol now there are a whole bunch of statements that go with conditionals if P then Q you see the statement here if P then Q converse statements are reverse it if Q then P a converse statement for if you are 16 then you may have a driver's license is if you have a driver's law if you it's okay for you to drive have a driver's license then you're at least 16 an inverse statement involves the negation of these the inverse notice it is in the form in the order again of P first and Q second however now we've got the not symbol so it's not P if not P then not Q that statement looks like if you are not 16 then you may not have a driver's license if you are not at least 16 it's not legal for you to have a driver's license contrapositive is the knots again with the Q first not if not Q then not P if it is not legal for you to have a driver's license then you are not at least 16 years old so that's an example of the conditional the converse the inverse and the contrapositive