Which expression is equal to \(A\setminus(B\cup C)\)?
Answer and explanation
Correct answer: \((A\setminus B)\cap(A\setminus C)\)
An element belongs to \(A\setminus(B\cup C)\) exactly when it is in A and is not in the union \(B\cup C\). Not being in a union means that it is in neither B nor C. Therefore the element is simultaneously in \(A\setminus B\) and in \(A\setminus C\), giving \((A\setminus B)\cap(A\setminus C)\). Equivalently, use \(A\cap(B\cup C)'=A\cap(B'\cap C')\).
Frequently asked questions
What is the correct answer to this question?
\((A\setminus B)\cap(A\setminus C)\)
Why is this the correct answer?
An element belongs to \(A\setminus(B\cup C)\) exactly when it is in A and is not in the union \(B\cup C\). Not being in a union means that it is in neither B nor C. Therefore the element is simultaneously in \(A\setminus B\) and in \(A\setminus C\), giving \((A\setminus B)\cap(A\setminus C)\). Equivalently, use \(A\cap(B\cup C)'=A\cap(B'\cap C')\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
