If U = {1,2,3,4} and A = ∅, what is A′?
Answer and explanation
Correct answer: U = {1,2,3,4}
The complement A′ consists of all elements of the universal set U that are not in A. Since A is the empty set, it contains no elements at all, so every element of U is outside A. Consequently, A′ = U = {1,2,3,4}. This illustrates the standard identity ∅′ = U, provided the complement is taken with respect to U. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
U = {1,2,3,4}
Why is this the correct answer?
The complement A′ consists of all elements of the universal set U that are not in A. Since A is the empty set, it contains no elements at all, so every element of U is outside A. Consequently, A′ = U = {1,2,3,4}. This illustrates the standard identity ∅′ = U, provided the complement is taken with respect to U. 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.
