Which expression is equal to \((A\cup B)\cap(A\setminus B)\)?
Answer and explanation
Correct answer: \(A\setminus B\)
Every element of \(A\setminus B\) is, by definition, an element of \(A\). Every element of \(A\) is contained in \(A\cup B\). Therefore all elements of \(A\setminus B\) already belong to the union, so intersecting with \(A\cup B\) removes nothing. Hence \((A\cup B)\cap(A\setminus B)=A\setminus B\).
Frequently asked questions
What is the correct answer to this question?
\(A\setminus B\)
Why is this the correct answer?
Every element of \(A\setminus B\) is, by definition, an element of \(A\). Every element of \(A\) is contained in \(A\cup B\). Therefore all elements of \(A\setminus B\) already belong to the union, so intersecting with \(A\cup B\) removes nothing. Hence \((A\cup B)\cap(A\setminus B)=A\setminus B\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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