If A ⊆ B ⊆ U, which relation is correct for their complements?
Answer and explanation
Correct answer: B' ⊆ A'
Because A is a subset of B, every element of A is also an element of B. Now take 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'. Hence B' ⊆ A'. This is the complement rule that reverses inclusion. Equality is not guaranteed unless A = B.
Frequently asked questions
What is the correct answer to this question?
B' ⊆ A'
Why is this the correct answer?
Because A is a subset of B, every element of A is also an element of B. Now take 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'. Hence B' ⊆ A'. This is the complement rule that reverses inclusion. Equality is not guaranteed unless A = B.
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.
