If A = {a, b, c, d, e}, how many subsets of A necessarily contain both a and b?
Answer and explanation
Correct answer: 8
The elements a and b are fixed as included in every required subset. The remaining elements c, d, and e are unrestricted: each one may either be included or omitted independently. Therefore, each of the three remaining elements gives two choices, and the total number of subsets is 2 × 2 × 2 = 2³ = 8. Hence option C 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 are fixed as included in every required subset. The remaining elements c, d, and e are unrestricted: each one may either be included or omitted independently. Therefore, each of the three remaining elements gives two choices, and the total number of subsets is 2 × 2 × 2 = 2³ = 8. 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.
