Determine whether the statement below makes sense or does not make sense. A cont

Question

Determine whether the statement below makes sense or does not make sense. A contrapositive statement can sometimes be false if its converse is false. Choose the correct choice below. This statement does make sense. The contrapositive statement is true for three combinations which includes when the converse statement is false or true. This statement does not make sense. The contrapositive statement is always false. This statement does not make sense. The contrapositive statement and the converse statement are not equivalent statements. The contrapositive statement is only false when the converse statement is true. This statement does make sense. The contrapositive statement and converse statement are both the same type of compound statement.

Explanation / Answer

For p -> q, contrapositive is ~q -> ~p and converse is q -> p

The contrapositive is false only if ~q is true and ~p is false.

Then q is false and p is true and q -> p is false -> true which is always true.

Thus the statement does not make sense. The contrapositive statatement and the converse statement are not equivalent statements. The contrapositive statement is only false when the converse statement is true.

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