Let U = {x ∈ ℕ : x ≤ 32} and A = {x ∈ U : x = 2^k for some k ∈ ℕ₀}. What is n(A′)?
Advertisement
Answer and explanation
Correct answer: 26
The universal set U contains the natural numbers from 1 through 32, so n(U) = 32. Since k belongs to ℕ₀, the relevant powers are 2⁰, 2¹, 2², 2³, 2⁴ and 2⁵, giving A = {1, 2, 4, 8, 16, 32}. Thus n(A) = 6. The complement A′ contains all elements of U that are not in A, so n(A′) = n(U) − n(A) = 32 − 6 = 26.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
The universal set U contains the natural numbers from 1 through 32, so n(U) = 32. Since k belongs to ℕ₀, the relevant powers are 2⁰, 2¹, 2², 2³, 2⁴ and 2⁵, giving A = {1, 2, 4, 8, 16, 32}. Thus n(A) = 6. The complement A′ contains all elements of U that are not in A, so n(A′) = n(U) − n(A) = 32 − 6 = 26.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
Advertisement