A conditional proposition that is true because the hypothesis is false is said to be trivially true conditionally true true by default vacuously true
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Decide whether each statement is true or false, and explain why. Given that $\sim p$ is false and $q$ is false, the conditional $p \rightarrow q$ is true.
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Which one of the following is a true statement? In the implication "A implies B", if the hypothesis A is true, then "A implies B" ought to be true (regardless of the truth value of B). In the implication "A implies B", if the hypothesis A is false, then we say that the implication "A implies B" is vacuously false. If x is a real number, then "0 ≤ x and 0 ≥ x" is always true. The equivalence "A ↔ B" is true if and only if A and B have the same truth value. All of the given statements are false. In the implication "A implies B", if the hypothesis A is false and the conclusion B is false, then "A implies B" ought to be false.
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Decide whether each statement is true or false, and explain why. Given that $\sim p$ is true and $q$ is false, the conditional $p \rightarrow q$ is true.
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