<Dd> "There exists a cat that is not a mammal ." If the negation is true, the original proposition (and by extension the contrapositive) is false . Here, of course, the negation is false . </Dd> <P> Note that if P → Q (\ displaystyle P \ rightarrow Q) is true and we are given that Q is false, ¬ Q (\ displaystyle \ neg Q), it can logically be concluded that P must be false, ¬ P (\ displaystyle \ neg P). This is often called the law of contrapositive, or the modus tollens rule of inference . </P> <P> Consider the Euler diagram shown . According to this diagram, if something is in A, it must be in B as well . So we can interpret "all of A is in B" as: </P> <Dl> <Dd> A → B (\ displaystyle A \ to B) </Dd> </Dl>

If p implies q then not q implies not p