Question

Question: Write the converse, inverse, and contrapositive of the following statement: "If I study for my math test, then I will get a good grade."

Answer 1

A conditional statement consists of two parts, a hypothesis p in the “if” clause and a conclusion q in the “then” clause, or mathematically you can write
`p\rightarrow q`.

In your example "If I study for my math test, then I will get a good grade" the hypothesis is p="I study for my math test" and the conclusion q="I will get a good grade".

To form the converse of the conditional statement, interchange the hypothesis and the conclusion (
`q\rightarrow p`).

In your case the converse statement is "If I will get a good mark, then I study for my math test."

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion (
`\\eg p\rightarrow \\eg q`).

In your case the inverse statement is "If I do not study for my math test, then I will not get a good mark."

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement (
`\\eg q\rightarrow \\eg p`).

In your example the contrapositive statement is "If I will not get a good mark, then I do not study for my math test."