Is "If A then B" equal to "B if and only if A"?
Is "If A then B" equal to "B if and only if A"?
Is "If A then B" equal to "B if and only if A"?
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The first statement only tells you when B is true. It says nothing about when it is false. The second statement both tells you when B is true (if A) and when it is not (only if A). Therefore, the two statements cannot be equal.