Question

1)Let the Universal Set, S, have 97 elements. A and B are subsets of S. Set A contains 45 elements and Set B contains 18 elements. If Sets A and B have 1 elements in common, how many elements are in A but not in B?

2)Let the Universal Set, S, have 178 elements. A and B are subsets of S. Set A contains 72 elements and Set B contains 95 elements. If Sets A and B have 39 elements in common, how many elements are in B but not in A?

3 Let the Universal Set, S, have 129 elements. A and B are subsets of S. Set A contains 92 elements and Set B contains 17 elements. If Sets A and B have 2 elements in common, how many elements are in neither A nor B?

Answer #1

1) number of elements in A but not in B = number of elements in A - number of elements in A and B = 45 - 1 = 44

2) number of elements in B but not in A = number of elements in B - number of elements in A and B = 95 - 39 = 56

3) number of elements in A or B = number of elements in A + number of elements in B - number of elements in A and B = 92 + 17 - 2 = 107

number of elements in neither A nor B = total elements - number of elements in A or B = 129 - 107 = 22

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