In a Venn diagram, what set is (A ∩ B) ∪ (A ∩ Bᶜ) equal to?
Answer and explanation
Correct answer: A
Use the distributive law for sets: \((A\cap B)\cup(A\cap B^c)=A\cap(B\cup B^c)\). A set and its complement together form the universal set, so \(B\cup B^c=U\). Hence the expression becomes \(A\cap U=A\). In a Venn diagram, the two terms divide A into its parts inside and outside B, so option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
A
Why is this the correct answer?
Use the distributive law for sets: \((A\cap B)\cup(A\cap B^c)=A\cap(B\cup B^c)\). A set and its complement together form the universal set, so \(B\cup B^c=U\). Hence the expression becomes \(A\cap U=A\). In a Venn diagram, the two terms divide A into its parts inside and outside B, so option A is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
