Question

Let the number of elements in sets A and B be five and two, respectively. Then the number of subsets of each having at least 3 and at most 6 elements is:

a. 26
b. 56
c. 64
d. 32

Answer 1

The number of subsets of sets A and B that have at least 3 and at most 6 elements is 29.

Step-by-step explanation:

To find the number of subsets of set A and B that have at least 3 and at most 6 elements, we can use the formula for the number of subsets of a set with n elements, which is 2^n. Set A has 5 elements, so it has 2^5 = 32 subsets. Set B has 2 elements, so it has 2^2 = 4 subsets. However, we are only interested in the subsets that have at least 3 and at most 6 elements. For set A, there are no subsets that have fewer than 3 elements, but there are 5 subsets that have exactly 3 elements, 10 subsets that have exactly 4 elements, 10 subsets that have exactly 5 elements, and 2 subsets that have exactly 6 elements. So in total, set A has 5 + 10 + 10 + 2 = 27 subsets that have at least 3 and at most 6 elements. For set B, there are no subsets that have fewer than 3 elements, but there is 1 subset that has exactly 3 elements and 1 subset that has exactly 4 elements. So in total, set B has 1 + 1 = 2 subsets that have at least 3 and at most 6 elements. Therefore, the answer is 27 + 2 = 29.