# Math Help - [SOLVED] Logical Laws and Equivalence

1. ## [SOLVED] Logical Laws and Equivalence

Hi,

Is this the right way to show that (~(p V q) => r) is logically equivalent to (p V q) V r.

(~(p V q) => r)
<==> (~~(p V q) V r) Implication Laws.
<==> (p V q) V r Double Negation.

Can someone check it for me and prehaps correct me?

Thanks for help.

2. ## Logic Laws

Hello kurac
Originally Posted by kurac
Hi,

Is this the right way to show that (~(p V q) => r) is logically equivalent to (p V q) V r.

(~(p V q) => r)
<==> (~~(p V q) V r) Implication Laws.
<==> (p V q) V r Double Negation.

Can someone check it for me and prehaps correct me?

Thanks for help.
Provided you can assume that $(p \Rightarrow q) \equiv (\neg p \vee q)$ your proof is fine. An alternative way would be to set up truth tables for $\neg(p \vee q) \Rightarrow r$ and $(p\vee q) \vee r$ and show that they produce the same output.