If A ⊆ U, which statement about A′ ⊆ U is correct?
Answer and explanation
Correct answer: A′ ⊆ U is always true
The complement A′ is defined as the set of elements of U that are not in A. Therefore every element of A′ already belongs to U, which directly gives A′ ⊆ U. The other statements are not always true: A′ may not be contained in A, U may contain elements of A, and A′ equals A only in special cases. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
A′ ⊆ U is always true
Why is this the correct answer?
The complement A′ is defined as the set of elements of U that are not in A. Therefore every element of A′ already belongs to U, which directly gives A′ ⊆ U. The other statements are not always true: A′ may not be contained in A, U may contain elements of A, and A′ equals A only in special cases. 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.
