If A ⊆ B, how is the statement B' ⊆ A' according to the Venn diagram?
Answer and explanation
Correct answer: True
If A is a subset of B, every element of A is also contained in B. Therefore, any element that is outside B cannot be in A; otherwise it would simultaneously be in A and outside B, contradicting A ⊆ B. Hence every element of B' belongs to A', so B' ⊆ A'. This is the contrapositive form of subset inclusion, and option A is correct.
Frequently asked questions
What is the correct answer to this question?
True
Why is this the correct answer?
If A is a subset of B, every element of A is also contained in B. Therefore, any element that is outside B cannot be in A; otherwise it would simultaneously be in A and outside B, contradicting A ⊆ B. Hence every element of B' belongs to A', so B' ⊆ A'. This is the contrapositive form of subset inclusion, and option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
