Stephanie W.

asked • 03/18/21

Use laws of logic to prove ¬ ( p → ¬ q ) ∨ ( q ∧ ( p ∨ ¬ q)) is equivalent to ( p and q)

Please write a detailed answer using the laws used to get to (p and q)

1 Expert Answer


Alec C. answered • 03/22/21

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Stephanie W.

p ∧ (q ∨ ( q ∧ ( p ∨ ¬ q))) What law is used here? associative and ? Also is there a different way to do it?


Alec C.

At that step I regrouped the parentheses, which is just the associative law. Nothing else at that step. I'm sure it's possible to solve this by working on the right side, but I think the way I did it above is probably the fastest/simplest way to do this problem.


Alex V.

I don't think the associative law let's you move the parentheses like that. However, you can use the distributive laws to move from (p ∧ q) ∨ ( q ∧ ( p ∨ ¬ q)) to q ∧ (p ∨ ( p ∨ ¬ q)).


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