My Math Forum Negation & Simplification of Proposition

 Calculus Calculus Math Forum

 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
Senior Member

Joined: Oct 2009

Posts: 439
Thanks: 147

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
Newbie

Joined: Feb 2018
From: USA

Posts: 2
Thanks: 0

Quote:
 Originally Posted by Micrm@ss Not correct.

Thank you.

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

February 18th, 2018, 09:05 AM   #4
Senior Member

Joined: Sep 2015
From: USA

Posts: 2,090
Thanks: 1086

Quote:
 Originally Posted by GEXDRF Thank you. Does $$∀_x(¬p(x) ∨ ¬ q(x))$$ require simplification?
it's a bit cleaner as $\forall_x ~(p(x) \wedge q(x))$

 Thread Tools Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top