If A = {a, b, c, d, e}, how many subsets of A contain both a and b?
Advertisement
Answer and explanation
Correct answer: 8
The elements a and b must be included in every required subset, so their choices are fixed. The remaining elements c, d, and e are each optional: each can either be included or excluded. Thus there are 2 choices for each of three independent elements, giving 2³ = 8 subsets. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The elements a and b must be included in every required subset, so their choices are fixed. The remaining elements c, d, and e are each optional: each can either be included or excluded. Thus there are 2 choices for each of three independent elements, giving 2³ = 8 subsets. Therefore, option A 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