[SOLVED] Logical Laws and Equivalence

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• Mar 23rd 2009, 01:57 AM
kurac
[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.
• Mar 23rd 2009, 03:12 AM
Grandad
Logic Laws
Hello kurac
Quote:

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.

Grandad
• Mar 23rd 2009, 03:21 AM
kurac
Yep, i assumed that from one of the Implication laws.

Thanks Grandad :)