Question

The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {2, 3, 4, 5, 6} and B = {5, 6, 7, 8, 9}, find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) (a) A ∩ B (b) A ∪ B (c) A' (d) B'

Answer 1

a) {5, 6}

b) {2, 3, 4, 5, 6, 7, 8, 9}

c) {0, 1, 7, 8, 9}

d) {0, 1, 2, 3, 4}

Explanation:

The intersection of sets is the set of elements common to both. The union of sets is the set of all elements that are part of either set. The complement of a set is the set of elements in the universal set that are not in the set of interest.

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A∩B

{2,3,4,5,6} ∩ {5,6,7,8,9} = {5, 6}

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A ∪ B

{2,3,4,5,6} ∪ {5,6,7,8,9} = {2,3,4,5,6,7,8,9}

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A'

U -A = {0,1,2,3,4,5,6,7,8,9} -{2,3,4,5,6} = {0,1,7,8,9}

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B'

U -B = {0,1,2,3,4,5,6,7,8,9} -{5,6,7,8,9} = {0,1,2,3,4}