Explanation


Solve this problem by brute force, but be systematic about it. Set Y has a finite number of elements, so list them out and start finding the products when those elements are multiplied by positive multiples of 5. Set Y = {3, 5, 7, 11, 13, 17, 19}, so multiplying by 5—the first positive multiple of 5—yields 15, 25, 35, 55, 65, 85, and 95; that’s 7 elements for set Z thus far.

Multiplying by 10—the next positive integer multiple of 5—yields 3 more products, 30, 50, and 70. Multiplying by 15 yields two new products, 45 and 75; multiplying by 20 yields only one new product, 60. That’s a total of 13 elements for set Z so far. You already have 75 as a member of set Z, so multiplying by 25 yields no new products; multiplying by 30 yields the final new product, 90. Set Z thus consists of 14 elements: set Z = {15, 25, 30, 35, 45, 50, 55, 60, 65, 70, 75, 85, 90, 95}. If you got choice (E), you may have mistakenly included 2 as an element of set Y.

Hence Option B is the correct option.