# Thread: laws of propositional logic to simplify

1. ## laws of propositional logic to simplify

simplify the following using laws of propositional logic:

~[p --> ~(p ^ q)]

2. ## Re: laws of propositional logic to simplify

Originally Posted by mathman11
simplify the following using laws of propositional logic:

~[p --> ~(p ^ q)]
do you know what $\neg (a \rightarrow b)$ equals?

3. ## Re: laws of propositional logic to simplify

Hello, mathman11!

Simplify the following using laws of propositional logic:

. . $\displaystyle \sim \big[p \to \:\sim(p \wedge q)\big]$

$\displaystyle \begin{array}{cccccccccc}1. & \sim \big[p \to \:\sim(p \wedge q)\big] && 1. & \text{Given} \\ 2. & \sim\big[\sim p\: \vee \sim(p \wedge q)\big] && 2. & \text{Def. of Impl'n} \\ 3. & \sim\big[\sim p \vee (\sim p \:\vee \sim q)\big] && 3. & \text{DeMorgan} \\ 4. & \sim \big[(\sim p\:\vee \sim p)\:\vee \sim q\big] && 4 . & \text{Associative} \\ 5. & \sim\big(\sim p \:\vee \sim q\big) && 5. & \text{Identity prop.} \\ 6. & p \wedge q && 6. & \text{DeMorgan} \end{array}$

4. ## Re: laws of propositional logic to simplify

Thanks Soroban .That helped alot.I'm having a hard time remembering the specific laws itself. What are some techniques to remember them?