Question

1. Given thatA={1,2,3,4,5} and B={3,5,10,11,12} and such that U= AUB. I) list down the elements of U,A' and A'UB'. ii) how many subsets do set A have?​

Answer 1

• U = {1, 2, 3, 4, 5, 10, 11, 12}
• A' = {10, 11, 12}
• A'∪B' = {1, 2, 4, 10, 11, 12}
• A has 32 subsets

Explanation:

i) The union of the two sets is the list of elements that are in either. Duplicates are listed only once.

U = {1, 2, 3, 4, 5, 10, 11, 12}

A' = U - A = {10, 11, 12}

A'∪B' = {10, 11, 12}∪{1, 2, 4} = {1, 2, 4, 10, 11, 12}

__

ii) A has 5 elements, so has 2^5 = 32 subsets, including the empty set and the whole set.