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February 18th, 2018, 07:57 AM   #1
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Negation & Simplification of Proposition

I am attempting to negate and simplify this proposition:

$ ∃_x((p(x) ∧ q(x)) $

My attempt to solve this:

$$∀_x(¬p(x) ∨ ¬ q(x))$$

$$∀_x(p(x) ∧ q(x))$$

I'm not sure if I have correctly negated and simplified this proposition, so help would be greatly appreciated.
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February 18th, 2018, 08:36 AM   #2
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Originally Posted by GEXDRF View Post
I am attempting to negate and simplify this proposition:

$ ∃_x((p(x) ∧ q(x)) $

My attempt to solve this:

$$∀_x(¬p(x) ∨ ¬ q(x))$$
Correct.

Quote:
$$∀_x(p(x) ∧ q(x))$$
Not correct.
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February 18th, 2018, 08:46 AM   #3
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Originally Posted by Micrm@ss View Post

Not correct.

Thank you.

Does $$∀_x(¬p(x) ∨ ¬ q(x))$$ require simplification?
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February 18th, 2018, 09:05 AM   #4
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Quote:
Originally Posted by GEXDRF View Post
Thank you.

Does $$∀_x(¬p(x) ∨ ¬ q(x))$$ require simplification?
it's a bit cleaner as $\forall_x ~(p(x) \wedge q(x))$
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