I need help proving, using laws of propositional logic that $(p⟹q) ∨ (p⟹r) = p⟹(q∨r)$. I'm not sure which laws I need to use to prove their equivalence. Any help would be appreciated.
Showing $(p⟹q) ∨ (p⟹r) = p⟹(q∨r)$ are logically equivalent
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discrete-mathematics
logic
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0Use equiv between $a \to b$ and $\lnot a \lor b$. – 2017-01-29
1 Answers
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You need:
Implication
$P \rightarrow Q \Leftrightarrow \neg P \lor Q$
Commutation
$P \lor Q \Leftrightarrow Q \lor P$
Association
$P \lor (Q \lor R) \Leftrightarrow (P \lor Q) \lor R$
Idempotence
$P \lor P \Leftrightarrow P$