If A \ B ⊆ C and A ∩ B ⊆ C, which conclusion is necessarily true?
Answer and explanation
Correct answer: A ⊆ C
Every element of A is either outside B or inside B. Therefore A can be partitioned as A = (A \ B) ∪ (A ∩ B). Both parts are given to be subsets of C, and the union of subsets of C is also a subset of C. Consequently, A ⊆ C. No condition controls elements in B \ A, so B ⊆ C and A ∪ B ⊆ C do not necessarily follow.
Frequently asked questions
What is the correct answer to this question?
A ⊆ C
Why is this the correct answer?
Every element of A is either outside B or inside B. Therefore A can be partitioned as A = (A \ B) ∪ (A ∩ B). Both parts are given to be subsets of C, and the union of subsets of C is also a subset of C. Consequently, A ⊆ C. No condition controls elements in B \ A, so B ⊆ C and A ∪ B ⊆ C do not necessarily follow.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
