If A = {1, 2, 3, 4} and B = {1, 3}, how many subsets of A contain B as a subset?
Answer and explanation
Correct answer: 4
Any subset of A that contains B must include 1 and 3; these two elements are compulsory. The remaining elements of A are 2 and 4, and each may either be included or excluded independently. Thus there are 2 choices for 2 and 2 choices for 4, giving 2 × 2 = 2² = 4 possible subsets: {1,3}, {1,2,3}, {1,3,4}, and {1,2,3,4}. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Any subset of A that contains B must include 1 and 3; these two elements are compulsory. The remaining elements of A are 2 and 4, and each may either be included or excluded independently. Thus there are 2 choices for 2 and 2 choices for 4, giving 2 × 2 = 2² = 4 possible subsets: {1,3}, {1,2,3}, {1,3,4}, and {1,2,3,4}. 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.
