please state whether this is true/false:
Let p = true, q = false, r = true
$\neg r \implies (p \wedge \neg q) = true$ [correct?]
false $\implies$ true that will be true right?
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Seems correct to me. – Vedran Šego Jul 27 '13 at 02:20
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Yes. $A \rightarrow B$ is the same as $\neg A \vee B$, so if $A$ is false, $A \rightarrow B$ is true. – Alex Kocurek Jul 27 '13 at 02:21
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3Your conclusion is correct. In a way you wrote more than necessary. Since $\lnot r$ is false, it is irrelevant that $p\land \lnot q$ is true. The implication would be true even if $p\land \lnot q$ happened to be false. – André Nicolas Jul 27 '13 at 02:25
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Your conclusion, and reasoning, are correct. However, you did more truth evaluations than necessary. Since $\lnot r$ is false, it is irrelevant that $p\land \lnot q$ is true. The implication would hold even if $p\land \lnot q$ happened to be false.
André Nicolas
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