If A = {1, 2, 3, 4, 5, 6}, how many subsets can be formed using only the odd elements?
Answer and explanation
Correct answer: 8
The odd elements of A are 1, 3 and 5, so the relevant set has three elements. Each of these three elements has two independent choices in a subset: it may be included or excluded. Therefore the number of subsets is 2³ = 8. This count includes the empty subset, the three one-element subsets, the three two-element subsets, and the full set of odd elements. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The odd elements of A are 1, 3 and 5, so the relevant set has three elements. Each of these three elements has two independent choices in a subset: it may be included or excluded. Therefore the number of subsets is 2³ = 8. This count includes the empty subset, the three one-element subsets, the three two-element subsets, and the full set of odd elements. 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.
