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5. Given events A and B in the sample space S, simplify the following sets. You can carry out the calculations using the laws of set operations. Alternatively, you can use Venn diagrams to find the answers. a. AU(An B) b. (AU(An B))

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Answer #1

a)

A U (A n B)' =A U (A' U B') =(A u A' u B') =S u B' =S   (As A u A' =S cause a event and its complement are mutually exclusive and collectively exhaustive)

b)

(A u (A n B))' =((A u A) n (A u B))' =(A n (A n B))' =(A)' =A'

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