My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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!
WWRtelescoping is offline  
 
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.
Hoempa is offline  
February 18th, 2014, 04:21 AM   #3
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 6

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" />
HallsofIvy is offline  
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.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
complement, sets



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
p (B intersect (A complement)) finalight Algebra 1 March 27th, 2012 12:34 PM
Complement of Whole Space lu5t Real Analysis 3 May 31st, 2011 09:36 PM
complement of sets Ben92 Applied Math 1 February 7th, 2011 07:19 AM
the complement of a simple graph spellbinder Applied Math 3 October 11th, 2010 03:13 PM
orthonogonal complement tinynerdi Linear Algebra 1 May 3rd, 2010 07:53 AM





Copyright © 2019 My Math Forum. All rights reserved.