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 February 18th, 2018, 08:57 AM #1 Newbie   Joined: Feb 2018 From: USA Posts: 2 Thanks: 0 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.
February 18th, 2018, 09:36 AM   #2
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Quote:
 Originally Posted by GEXDRF 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.

February 18th, 2018, 09:46 AM   #3
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Quote:
 Originally Posted by Micrm@ss Not correct.

Thank you.

Does $$∀_x(¬p(x) ∨ ¬ q(x))$$ require simplification?

February 18th, 2018, 10:05 AM   #4
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Quote:
 Originally Posted by GEXDRF 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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