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What is a converse of a theorem that is an if-then statement? (1 point) The two parts are negated by using the word not. The if part and the then part switch places. The converse is the same as the original theorem. The converse of a theorem has no relationship to the original theorem.

Ask by Welch Elliott. in the United States
Mar 18,2025

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The converse of an if-then statement switches the "if" and "then" parts.

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The Deep Dive

The if part and the then part switch places. In other words, if a theorem is stated as "If A, then B," the converse would be "If B, then A." It's important to note that the truth of the original theorem does not guarantee the truth of its converse. In the realm of mathematics, while converses can be interesting to explore, they often lead to distinct truths. For example, in geometry, "If a figure is a square, then it is a rectangle" is true, but the converse "If a figure is a rectangle, then it is a square" is not necessarily true! This highlights the necessity of rigorous proof when working with converses.

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