Which of the following sets is equivalent to \(A\cup(B\cap C)\)?
Answer and explanation
Correct answer: \((A\cup B)\cap(A\cup C)\)
The second distributive law for sets is \(A\cup(B\cap C)=(A\cup B)\cap(A\cup C)\). To verify it elementwise, an element is on the left if it is in \(A\), or if it is in both \(B\) and \(C\). On the right, it must be in both unions, which gives exactly the same condition. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
\((A\cup B)\cap(A\cup C)\)
Why is this the correct answer?
The second distributive law for sets is \(A\cup(B\cap C)=(A\cup B)\cap(A\cup C)\). To verify it elementwise, an element is on the left if it is in \(A\), or if it is in both \(B\) and \(C\). On the right, it must be in both unions, which gives exactly the same condition. Therefore, 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).
