What is the contrapositive of the conditional statement 'If p, then q'?

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Multiple Choice

What is the contrapositive of the conditional statement 'If p, then q'?

The main idea is that the contrapositive of a conditional statement is formed by negating both parts and swapping them: If p then q is logically the same as If not q, then not p. This equivalence means the truth of the original statement is preserved in its contrapositive. For example, if “If a shape is a square, then it has four equal sides,” the contrapositive is “If the shape does not have four equal sides, then it is not a square.” This helps you see why the contrapositive works: denying q requires denying p as well. In this problem, the contrapositive of If p, then q is If not q, then not p. The other forms are different: If q, then p is the converse, and If not p, then not q is the inverse. The original statement is If p, then q.

The main idea is that the contrapositive of a conditional statement is formed by negating both parts and swapping them: If p then q is logically the same as If not q, then not p. This equivalence means the truth of the original statement is preserved in its contrapositive.

For example, if “If a shape is a square, then it has four equal sides,” the contrapositive is “If the shape does not have four equal sides, then it is not a square.” This helps you see why the contrapositive works: denying q requires denying p as well.

In this problem, the contrapositive of If p, then q is If not q, then not p. The other forms are different: If q, then p is the converse, and If not p, then not q is the inverse. The original statement is If p, then q.

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