If n(A−B)=0, n(B−C)=0 and n(A)>0, which relation must be true?
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Answer and explanation
Correct answer: A⊆C
A−B is empty exactly when every element of A belongs to B, so n(A−B)=0 implies A⊆B. Similarly, n(B−C)=0 implies B⊆C. Subset relations are transitive: if every element of A is in B and every element of B is in C, then every element of A is in C. Hence A⊆C must hold. The condition n(A)>0 does not change this conclusion.
Frequently asked questions
What is the correct answer to this question?
A⊆C
Why is this the correct answer?
A−B is empty exactly when every element of A belongs to B, so n(A−B)=0 implies A⊆B. Similarly, n(B−C)=0 implies B⊆C. Subset relations are transitive: if every element of A is in B and every element of B is in C, then every element of A is in C. Hence A⊆C must hold. The condition n(A)>0 does not change this conclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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