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 February 17th, 2014, 08:50 PM #1 Senior Member   Joined: Jan 2014 Posts: 196 Thanks: 3 A sets complement Given, , , and Find " /> Just visualizing this, I am sure the answer is Is the correct set notation, and what is given, would this be = P(A) - P(A \cap B)" /> ? thanks! February 18th, 2014, 02:23 AM #2 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 Re: A sets complement The set you want is which has area = P(A) - P(A \cap B)" />, yes. February 18th, 2014, 04:21 AM   #3
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Re: A sets complement

Quote:
 Originally Posted by WWRtelescoping Given, , , and Find " /> Just visualizing this, I am sure the answer is Is the correct set notation, and what is given, would this be = P(A) - P(A \cap B)" /> ? thanks!
??? = P(A)- P(A\cap B)" />, yes, but you originally asked about " />

Imagine 10 objects in the "universe". There are 4 in A, 5 in B, and 3 in both. So there are 4- 3= 1 that are in A but not in B. That would be = 1" />. There are 5- 3= 2 that are in B but not in A so 10- 2= 8 that are in A or not in B. That is = 8" /> February 18th, 2014, 11:15 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,035 Thanks: 2271 A = A ? (B ? B') = (A ? B) ? (A ? B'), which is a union of disjoint sets. Hence P(A) = P(A ? B) + P(A ? B'), and so P(A ? B') = P(A) - P(A ? B) = .4 - .3 = .1. Similarly, P(A' ? B) = P(B) - P(A ? B) = .5 - .3 = .2. As A ? B' = (A' ? B)', P(A ? B') = 1 - P(A' ? B) = 1 - .2 = .8. Neither calculation needs all the information given in the question. Tags complement, sets 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 finalight Algebra 1 March 27th, 2012 12:34 PM lu5t Real Analysis 3 May 31st, 2011 09:36 PM Ben92 Applied Math 1 February 7th, 2011 07:19 AM spellbinder Applied Math 3 October 11th, 2010 03:13 PM tinynerdi Linear Algebra 1 May 3rd, 2010 07:53 AM

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