# Show that p → q ≡ (∼ p) ∨ q

## 1 Answer

Toolbox:
• If $p$ and $q$ are two simple statements $p\wedge$ is the conjunction of $p$ and $q$ and $p \vee q$ is the disjunction .Negation of a statement $p$ is denoted by $\sim p$
• Rules for conjunction :
• $A_3$: The statement $p\vee q$ has the truth value $F$ whenever both $p$ and $q$ have the truth value $F$.
• $A_4$: The statement $p\vee q$ has the truth value $T$ whenever either $p$ or $q$ or both have the truth value $T$
The last two columns of the truth table are identical.
$\therefore p\rightarrow q \equiv (\sim p)\vee q$
answered Sep 13, 2013

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