set theory examples

# set theory examples - 1 Let = cfw_1 2 10 let A be the even...

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1. Let = {1, 2, . . . , 10}, let A be the even numbers in , let B be the prime numbers In , and let C be the numbers larger than 3 in . Find , and C A B A C C C , , , B A B A . 2. Prove the following: P(A C B ) = P(A) P(A B). 3. A 5th grade teacher is looking over the grade distribution for her 32 students. She notices that 3 students “aced” Math, Science and English while 13 did not ace any of the three subjects. There were 7 who aced Science and English, 4 who aced Science and Math, and 3 who aced Math and English. 11 total aced Science and 9 total aced Math. Draw a Venn Diagram with the numbers filled in. 4. Suppose a city has three newspapers, The Times, The Herald and The Examiner. Circulation information indicates that 47% of households get the Times, 33.4% get The Herald, 34.6% get The Examiner, 11.9% get The Times and The Herald, 15.1% get The Times and The Examiner, 10.4% get The Herald and The Examiner and 4.8% get all three. If a household is selected at random, what is the probability that the household receives: (a) either The Times or The Herald, but not both?

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