Which option is the contrapositive of the conditional statement P -> Q?

Which option is the contrapositive of the conditional statement P -> Q?

• A. Not P -> Not Q
• B. Not Q -> Not P
• C. Q -> P
• D. P -> Q

Answer: (B)

When a conditional says “If P then Q,” the statement you form to test equivalence is the contrapositive: not Q implies not P. It uses the same truth value as the original, just with the order flipped and both parts negated. Think of P as a situation that leads to Q. If that implication is true, then whenever Q is not true, P can’t be true either—so not Q would force not P. That’s why not Q -> not P is the contrapositive. For a quick check with a concrete idea: if “studying leads to passing the course” (P -> Q), then the contrapositive is “if you do not pass the course (not Q), then you did not study (not P).” These two statements always share the same truth value. The other forms are different transformations: swapping P and Q gives the converse, which isn’t guaranteed to be true the same way; negating both parts without swapping gives the inverse, which also isn’t equivalent to the original.

When a conditional says “If P then Q,” the statement you form to test equivalence is the contrapositive: not Q implies not P. It uses the same truth value as the original, just with the order flipped and both parts negated.

Think of P as a situation that leads to Q. If that implication is true, then whenever Q is not true, P can’t be true either—so not Q would force not P. That’s why not Q -> not P is the contrapositive.

For a quick check with a concrete idea: if “studying leads to passing the course” (P -> Q), then the contrapositive is “if you do not pass the course (not Q), then you did not study (not P).” These two statements always share the same truth value.

The other forms are different transformations: swapping P and Q gives the converse, which isn’t guaranteed to be true the same way; negating both parts without swapping gives the inverse, which also isn’t equivalent to the original.