Question

Which one of the sets given below is the power set of the set 1,2,3?

1) {1,2,3}
2) {1}
3) {2}
4) {3}
5) {1,2}
6) {1,3}
7) {2,3}
8) {}

Answer 1

The power set of the set {1,2,3} includes all subsets of the set, including the empty set and the set itself, totaling 2^3 = 8 subsets.

Step-by-step explanation:

The question asks for the power set of the set {1,2,3}. A power set is a set of all subsets of a set, including the empty set and the set itself. Let's enumerate these subsets:

• Empty set: {}
• {1}
• {2}
• {3}
• {1,2}
• {1,3}
• {2,3}
• The set itself: {1,2,3}

Therefore, the power set of the set {1,2,3} is {{}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}. This power set contains 23 = 8 subsets, because the original set has 3 elements, and the power set of a set with n elements contains 2n subsets.