I'm wondering whether $((A\to B)\land (\lnot A \to C)) \iff (A\lor C)$ is correct or not.
Is $((A\to B)\land (\lnot A \to C))\equiv (A\lor C)$?
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propositional-calculus
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10Have you tried using a truth-table? If not, what else have you tried? – 2017-01-08
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0Do you mean B or C (not A or C)? – 2017-01-08
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1Since $(\lnot A \to C) \equiv (A\lor C)$, we have $((A\to B) \land (\lnot A \to C)) \rightarrow (A\lor C))$, But not vice-versa. So the biconditional is wrong. – 2017-01-08
2 Answers
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Hint:
$\neg A \Rightarrow C$ is equivalent to $A\vee C$.
2
Hint: Consider the case $A:\text{true}$, $B:\text{false}$, $C:\text{any}$