# Thread: Prove Statement is logically equivalent using laws of logic

1. ## Prove Statement is logically equivalent using laws of logic

Hello Everyone,

I just stuck-up while solving the following question:

Verify this statement is logically equivalent using laws of logic :

~(P disjunction q) disjunction (~p ^ q) = ~ p

Note: here is used word disjunction instead of symbol.

I need your help and support to solve this problem.
Thanks.

2. $\displaystyle \sim (p \vee q) \vee \left( { \sim p \wedge q} \right) \equiv \left( { \sim p \wedge \sim q} \right) \vee \left( { \sim p \wedge q} \right)$
$\displaystyle \left( { \sim p \wedge \sim q} \right) \vee \left( { \sim p \wedge q} \right) \equiv \sim p \wedge \underbrace {\left( { \sim q \vee q} \right)}_{true} \equiv \sim p$

3. ## Prove statement is true using laws of logic.

Hello galactus,

Thanks for Your reply, but if you read my question, i asked to prove this statement using "Laws Of Logic" not by using truth table. I know how to prove it using truth table table.

Kaleem.

4. Originally Posted by Kaleem Qureshi
Hello galactus,

Thanks for Your reply, but if you read my question, i asked to prove this statement using "Laws Of Logic" not by using truth table. I know how to prove it using truth table table.

Kaleem.
I believe Plato already did this for you in post #2 using De Morgan's law, the Distributive law, and the Absorption law.