SME
Discrete Mathematics
Logic and proofs
Use this for “Which statement is equivalent to: if it rains, the game is cancelled?”
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Is each statement equivalent to p → q?
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p → q is false only when p is true and q is false; the contrapositive is false in exactly that row too.
Assumptions
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In p → q, p is the hypothesis and q the conclusion: “if it rains (p), the game is cancelled (q).”
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p → q is false only when p is true and q is false; in the other three rows it is true.
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Two statements are equivalent when they are true in exactly the same rows of a truth table.
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More problem types
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