Question:
If A and B are two non-empty sets, then \((A\cup B)-(A\cap B)=\)
If A and B are two non-empty sets, then \((A\cup B)-(A\cap B)=\)
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The symmetric difference consists of the two non-overlapping portions of a Venn diagram.
Updated On: Jun 15, 2026
- \((A-B)\cup(B-A)\)
- \((A-B)\cap(B-A)\)
- \(A\cup B\)
- \(A\cap B\)
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The Correct Option is A
Solution and Explanation
Concept:
The expression
\[
(A\cup B)-(A\cap B)
\]
is called the symmetric difference of sets \(A\) and \(B\).
Step 1: Interpret the given expression.
The set \(A\cup B\) contains all elements that belong to \(A\) or \(B\). The set \(A\cap B\) contains the common elements. Subtracting the common elements leaves only those elements that belong exclusively to one set.
Step 2: Express the remaining elements.
Elements belonging only to \(A\) form \[ A-B \] Elements belonging only to \(B\) form \[ B-A \] Taking their union, \[ (A-B)\cup(B-A) \] which is exactly the symmetric difference. \centerline{{\((A-B)\cup(B-A)\)}}
Step 1: Interpret the given expression.
The set \(A\cup B\) contains all elements that belong to \(A\) or \(B\). The set \(A\cap B\) contains the common elements. Subtracting the common elements leaves only those elements that belong exclusively to one set.
Step 2: Express the remaining elements.
Elements belonging only to \(A\) form \[ A-B \] Elements belonging only to \(B\) form \[ B-A \] Taking their union, \[ (A-B)\cup(B-A) \] which is exactly the symmetric difference. \centerline{{\((A-B)\cup(B-A)\)}}
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