How many proper subsets does the set {4, 5, 6, 7, 8} have?

Correct answer: b 31

n = 5; 2⁵ − 1 = 32 − 1 = 31, because the set itself is left out.

Why the other options are wrong

• a 10: Doing 2 × 5 is a slip; each element is either taken or not, which gives 2⁵.
• c 32: This is the count of all subsets, 2⁵; proper subsets exclude the set itself.
• d 33: This is one more than 2⁵; the count is 2⁵ − 1, not 2⁵ + 1.