If A = {1,{2}}, how many subsets does A have?
Advertisement
Answer and explanation
Correct answer: 4
The set A has exactly two elements: the number 1 and the set {2}. The inner set {2} counts as one element of A; the number 2 is not separately an element of A. A set with n elements has 2ⁿ subsets, so here the number is 2² = 4. Explicitly, the subsets are ∅, {1}, {{2}}, and {1,{2}}. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The set A has exactly two elements: the number 1 and the set {2}. The inner set {2} counts as one element of A; the number 2 is not separately an element of A. A set with n elements has 2ⁿ subsets, so here the number is 2² = 4. Explicitly, the subsets are ∅, {1}, {{2}}, and {1,{2}}. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement