Question

If a conditional statement p-a is true, and its converse q-p is false, which related conditionals are also false?

a) Inverse and contrapositive
b) Inverse and biconditional
c) Contrapositive and biconditional
d) None of the above

Answer 1

The contrapositive and biconditional conditionals are also false.

Therefore, the correct answer is: option c) Contrapositive and biconditional

Step-by-step explanation:

In a conditional statement, the inverse and contrapositive are related to the original statement.

The inverse of a conditional statement switches the hypothesis and conclusion and negates both.

The contrapositive of a conditional statement switches the hypothesis and conclusion and negates both.

In this case, if the original statement p-a is true and its converse q-p is false, it means that a and p are related.

Therefore, the contrapositive, which is based on the relation of a and p, is also false.

The biconditional, on the other hand, relates p and a in both directions, so if the original statement is true and its converse is false, it means that the biconditional is also false. Therefore, the answer is c) Contrapositive and biconditional.