If \(A\cup(A\cap B)=A\), which law of sets does this represent?
Answer and explanation
Correct answer: Absorption law
The identity \(A\cup(A\cap B)=A\) is the absorption law. Since \(A\cap B\) is always a subset of \(A\), taking its union with \(A\) cannot add any new element. Consequently, the result remains \(A\). The distributive law expands an operation across parentheses, while De Morgan’s laws involve complements. Therefore option A is unambiguously correct. The companion absorption identity is \(A\cap(A\cup B)=A\).
Frequently asked questions
What is the correct answer to this question?
Absorption law
Why is this the correct answer?
The identity \(A\cup(A\cap B)=A\) is the absorption law. Since \(A\cap B\) is always a subset of \(A\), taking its union with \(A\) cannot add any new element. Consequently, the result remains \(A\). The distributive law expands an operation across parentheses, while De Morgan’s laws involve complements. Therefore option A is unambiguously correct. The companion absorption identity is \(A\cap(A\cup B)=A\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
