If A = {1,2,3,4,5,6}, how many elements of P(A) are subsets containing at least 2 elements?
Answer and explanation
Correct answer: 57
A six-element set has 2⁶ = 64 total subsets. The subsets with fewer than two elements are the empty subset, counted by C(6,0)=1, and the six one-element subsets, counted by C(6,1)=6. Thus 7 subsets have fewer than two elements. Subtracting them from all subsets gives 64 − 7 = 57 subsets containing at least two elements. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
57
Why is this the correct answer?
A six-element set has 2⁶ = 64 total subsets. The subsets with fewer than two elements are the empty subset, counted by C(6,0)=1, and the six one-element subsets, counted by C(6,1)=6. Thus 7 subsets have fewer than two elements. Subtracting them from all subsets gives 64 − 7 = 57 subsets containing at least two elements. Therefore option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
