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 February 18th, 2018, 07:57 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, 08:36 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, 08:46 AM   #3
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 Originally Posted by Micrm@ss Not correct.

Thank you.

Does $$∀_x(¬p(x) ∨ ¬ q(x))$$ require simplification? February 18th, 2018, 09:05 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 $\forall_x ~(p(x) \wedge q(x))$ Tags negation, proposition, simplification Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rafik165M Number Theory 2 November 16th, 2014 12:08 PM danoc93 Applied Math 4 October 1st, 2013 02:06 PM FloorPlay Applied Math 7 September 6th, 2012 04:46 AM Axel Applied Math 3 April 19th, 2011 07:15 PM wannabe1 Applied Math 4 October 11th, 2009 01:00 PM

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