CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
A = {x : x is an integer, −3 ≤ x ≤ 4} and B = {x² : x ∈ A}. How many elements does B have, and what is the sum of the elements of B?
Squaring the integers from −3 to 4 gives 9, 4, 1, 0, 1, 4, 9 and 16. Because a set lists each value once, B = {0, 1, 4, 9, 16}, which has 5 elements with a sum of 30.
- A8 elements, sum 44
- B5 elements, sum 30Correct
- C5 elements, sum 25
- D4 elements, sum 14
Explanation
A = {−3,−2,−1,0,1,2,3,4}. Squares are 9,4,1,0,1,4,9,16; as a set, duplicates collapse to {0,1,4,9,16}. That is 5 elements with sum 0+1+4+9+16 = 30. Option 8 elements counts repeated values, and sum 44 would be the sum with repeats... that sum is 44, confirming the error.
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