If A = {a, b, c, d}, how many subsets of A have at least two elements?
Answer and explanation
Correct answer: 11
A set with four elements has 2^4 = 16 total subsets. The subsets having fewer than two elements are the empty set, which has zero elements, and the four singleton subsets {a}, {b}, {c}, and {d}; therefore there are 1 + 4 = 5 excluded subsets. The number with at least two elements is 16 - 5 = 11. Equivalently, one may add C(4,2) + C(4,3) + C(4,4) = 6 + 4 + 1 = 11.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
A set with four elements has 2^4 = 16 total subsets. The subsets having fewer than two elements are the empty set, which has zero elements, and the four singleton subsets {a}, {b}, {c}, and {d}; therefore there are 1 + 4 = 5 excluded subsets. The number with at least two elements is 16 - 5 = 11. Equivalently, one may add C(4,2) + C(4,3) + C(4,4) = 6 + 4 + 1 = 11.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
