SOLUTION: Which of the following statements is a TRUE statement? (A) The set {a, b, c} has three subsets. (B) The set {a, b, c} has five subsets. (C) The set {a, b, c} has seven subsets.

Question 1095094: Which of the following statements is a TRUE statement? (A) The set {a, b, c} has three subsets.
(B) The set {a, b, c} has five subsets.
(C) The set {a, b, c} has seven subsets.
(D) The set {a, b, c} has eight subsets.
Answer by greenestamps(13214) (Show Source): You can put this solution on YOUR website!

The number of subsets of a set containing n elements is 2^n. In your set with three elements, the number of subsets is 2^3 = 8.

To see why the number of subsets of a set containing n elements is 2^n, imagine the process of forming a subset. You go down the list of elements in the set, and for each one you choose either to include it in the subset or not. That's 2 choices for each of the n elements; all together, by the fundamental counting principle, the number of combinations of choices you can make -- and therefore the number of different subsets you can form -- is 2^n.
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