In logic, the contrapositive of p→q is what?

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Multiple Choice

In logic, the contrapositive of p→q is what?

The essential idea is that a contrapositive flips the direction of a conditional statement and negates both parts. If p → q is true, then not q → not p is also true, and they share the same truth value. That makes the contrapositive the correct way to restate the implication with negations. So, the contrapositive is: If not q, then not p. This form is useful in proofs because proving the contrapositive can sometimes be easier than proving the original implication, and it guarantees the same truth as the original statement. For a quick intuition, think of a rule like: If you study hard, you will pass the exam. The contrapositive is: If you do not pass the exam, you did not study hard. This helps see why the contrapositive preserves logical equivalence with the original statement.

The essential idea is that a contrapositive flips the direction of a conditional statement and negates both parts. If p → q is true, then not q → not p is also true, and they share the same truth value. That makes the contrapositive the correct way to restate the implication with negations.

So, the contrapositive is: If not q, then not p. This form is useful in proofs because proving the contrapositive can sometimes be easier than proving the original implication, and it guarantees the same truth as the original statement.

For a quick intuition, think of a rule like: If you study hard, you will pass the exam. The contrapositive is: If you do not pass the exam, you did not study hard. This helps see why the contrapositive preserves logical equivalence with the original statement.

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