If A = {a,b,c,d,e}, how many subsets in P(A) contain exactly one of a and b?
Answer and explanation
Correct answer: 16
There are two possibilities for the condition involving a and b: either a is included and b is excluded, or b is included and a is excluded. The remaining elements c, d, and e are unrestricted, so each can independently be included or excluded in 2³ ways. Hence the total number of subsets is 2 × 2³ = 16. Option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
There are two possibilities for the condition involving a and b: either a is included and b is excluded, or b is included and a is excluded. The remaining elements c, d, and e are unrestricted, so each can independently be included or excluded in 2³ ways. Hence the total number of subsets is 2 × 2³ = 16. 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.
