If U={1,2,…,14} and A={2,4,6,8,10,12,14}, how many ordered pairs are in A′×A?
Answer and explanation
Correct answer: 49
The universal set U has 14 elements. Set A contains the seven even numbers from 2 through 14, so its complement A′ contains the seven odd numbers {1,3,5,7,9,11,13}. The Cartesian product A′×A consists of ordered pairs whose first element is chosen from A′ and second from A. Therefore, n(A′×A)=n(A′)×n(A)=7×7=49. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
49
Why is this the correct answer?
The universal set U has 14 elements. Set A contains the seven even numbers from 2 through 14, so its complement A′ contains the seven odd numbers {1,3,5,7,9,11,13}. The Cartesian product A′×A consists of ordered pairs whose first element is chosen from A′ and second from A. Therefore, n(A′×A)=n(A′)×n(A)=7×7=49. Hence, option A is correct.
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.
