If \(A\cap(A\cup B)=A\), which law of sets does this represent?
Answer and explanation
Correct answer: Absorption law
The expression \(A\cap(A\cup B)=A\) is the second standard form of the absorption law. Every element of \(A\) is automatically in \(A\cup B\), so intersecting \(A\cup B\) with \(A\) leaves exactly \(A\). The commutative law changes the order of operations or sets, and the associative law changes grouping; neither explains this reduction. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
Absorption law
Why is this the correct answer?
The expression \(A\cap(A\cup B)=A\) is the second standard form of the absorption law. Every element of \(A\) is automatically in \(A\cup B\), so intersecting \(A\cup B\) with \(A\) leaves exactly \(A\). The commutative law changes the order of operations or sets, and the associative law changes grouping; neither explains this reduction. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
