Answer to Question #156613 in Discrete Mathematics for ken

Question

Let S be the following statement. “If it is raining, then the ground is wet.” Translate the S into symbol State in English the converse of S State in English the contrapositive of S

Answer 1

Let A be a sentence "It is raining", and B be a sentence "The ground is wet". Then the statement S will take the form "If A then B" and can be written in symbols as

$(A\to B).$

The contrapositive of S is the statement $(\neg B \to \neg A)$.

In English: "If the ground is not wet, then it is not raining."

The converse of S is the statement $(B\to A)$.

In English: "If the ground is wet, then it is raining".