If A = {a, b, c, d, e}, how many subsets contain both a and b?
Answer and explanation
Correct answer: 8
Because both a and b must be present, they are fixed and do not create choices. Only the remaining three elements, c, d, and e, can be independently included or excluded. Therefore, there are 2³ = 8 possible subsets containing both required elements. They are obtained by combining {a,b} with any subset of {c,d,e}. Option D, 32, counts all subsets of A, while 4 incorrectly allows choices for only two remaining elements.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Because both a and b must be present, they are fixed and do not create choices. Only the remaining three elements, c, d, and e, can be independently included or excluded. Therefore, there are 2³ = 8 possible subsets containing both required elements. They are obtained by combining {a,b} with any subset of {c,d,e}. Option D, 32, counts all subsets of A, while 4 incorrectly allows choices for only two remaining elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
