For two sets A and B in a Venn diagram, which of the following statements is always true?
Answer and explanation
Correct answer: A ∩ B ⊆ A
By definition, A ∩ B contains precisely those elements that belong to both A and B. Every element belonging to both sets must certainly belong to A, so A ∩ B ⊆ A is always true. Option B reverses the usual inclusion relationship and is generally false. Option C is not generally valid because the two differences usually contain different elements. Option D is also not generally true because a set and its complement are normally different.
Frequently asked questions
What is the correct answer to this question?
A ∩ B ⊆ A
Why is this the correct answer?
By definition, A ∩ B contains precisely those elements that belong to both A and B. Every element belonging to both sets must certainly belong to A, so A ∩ B ⊆ A is always true. Option B reverses the usual inclusion relationship and is generally false. Option C is not generally valid because the two differences usually contain different elements. Option D is also not generally true because a set and its complement are normally different.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
