If U = {1, 2, ..., 32} and A = {x : x ∈ U, x is even}, how many ordered pairs are in A' × A'?
Answer and explanation
Correct answer: 256
The universal set U has 32 elements. Exactly 16 of them are even, so A contains 16 elements. The complement A' therefore contains the 16 odd numbers from 1 to 32. For any finite sets X and Y, n(X × Y) = n(X)n(Y). Hence n(A' × A') = 16 × 16 = 256. The order matters in a Cartesian product, and every first component can be paired with every second component.
Frequently asked questions
What is the correct answer to this question?
256
Why is this the correct answer?
The universal set U has 32 elements. Exactly 16 of them are even, so A contains 16 elements. The complement A' therefore contains the 16 odd numbers from 1 to 32. For any finite sets X and Y, n(X × Y) = n(X)n(Y). Hence n(A' × A') = 16 × 16 = 256. The order matters in a Cartesian product, and every first component can be paired with every second component.
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.
