If A = {a,b,c,d}, how many subsets in P(A) do not contain a?
Answer and explanation
Correct answer: 8
To form a subset of A that does not contain a, we may choose or reject each of the remaining elements b, c, and d independently. Each element gives 2 choices, so the total number of permitted subsets is 2 × 2 × 2 = 2³ = 8. These include the empty set and all subsets formed only from {b,c,d}. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
To form a subset of A that does not contain a, we may choose or reject each of the remaining elements b, c, and d independently. Each element gives 2 choices, so the total number of permitted subsets is 2 × 2 × 2 = 2³ = 8. These include the empty set and all subsets formed only from {b,c,d}. Therefore, 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.
