If the universal set U = {1, 2, 3, 4, 5} and A = {1, 3, 5}, what is the complement of A, denoted by A′?
Answer and explanation
Correct answer: A′ = {2, 4}
The complement of A is defined relative to the universal set U. It contains every element of U that is not an element of A. Starting with U = {1, 2, 3, 4, 5} and removing 1, 3, and 5 leaves {2, 4}. Therefore A′ = U \ A = {2, 4}, making option A correct. The universal set must always be identified before finding a complement.
Frequently asked questions
What is the correct answer to this question?
A′ = {2, 4}
Why is this the correct answer?
The complement of A is defined relative to the universal set U. It contains every element of U that is not an element of A. Starting with U = {1, 2, 3, 4, 5} and removing 1, 3, and 5 leaves {2, 4}. Therefore A′ = U \ A = {2, 4}, making option A correct. The universal set must always be identified before finding a complement.
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.
