For subsets A and B of a universal set U, if A ⊆ B, which relation between their complements is correct?
Answer and explanation
Correct answer: B' ⊆ A'
If A ⊆ B, every element of A is also an element of B. Consider any element x in B'. It is not in B. Since every element of A must lie in B, x cannot be in A either; therefore x belongs to A'. This proves B' ⊆ A'. Complementation reverses the direction of subset inclusion, so option B is correct. Equality is possible only in the special case A = B, not in general.
Frequently asked questions
What is the correct answer to this question?
B' ⊆ A'
Why is this the correct answer?
If A ⊆ B, every element of A is also an element of B. Consider any element x in B'. It is not in B. Since every element of A must lie in B, x cannot be in A either; therefore x belongs to A'. This proves B' ⊆ A'. Complementation reverses the direction of subset inclusion, so option B is correct. Equality is possible only in the special case A = B, not in general.
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.
