Question

True or false? If you took a true “if-then” statement, inserted a not in each clause, and reversed the clashes, the new statement would also be true

Answer 1

True

Explanation:

If you took a true if-then statement, inserted not in each clause and reversed the clauses you will have created the contrapositive. The contrapositive of an if-then statement has the same true value as the original statement.

Statement:

If p, then q.

Contrapositive:

If not q, then not p

If the statement is true, then the contrapositive is also true.

Answer 2

The statement would not necessarily be true after inserting "not" in each clause and reversing the clauses.

Consider the following true "if-then" statement:

If it rains, then the ground gets wet.

If we insert "not" in each clause and reverse the clauses, we get:

If it does not rain, then the ground does not get wet.

This statement is also true. However, if we consider the following true "if-then" statement:

If a number is even, then it is divisible by 2.

If we insert "not" in each clause and reverse the clauses, we get:

If a number is not even, then it is not divisible by 2.

This statement is not true. For example, 3 is not even, but it is still divisible by 2. Therefore, the statement that a true "if-then" statement, after inserting a not in each clause and reversing the clauses, will still be true is false in general.