The symmetric difference of A and B is not equal to
(a) \((A-B) \cap (B-A)\)
(b) \((A-B) \cup (B-A)\)
(c) \((A \cup B)-(A \cap B)\)
(d) \(\{(A \cup B)-A\} \cup \{(A \cup B)-B\}\)
Solution
Symmetric difference is defined as
\[ A \Delta B = (A-B)\cup(B-A) \]
Also,
\[ A \Delta B=(A\cup B)-(A\cap B) \]
and
\[ \{(A\cup B)-A\}\cup\{(A\cup B)-B\}=A\Delta B \]
But,
\[ (A-B)\cap(B-A)=\Phi \]
which is not equal to symmetric difference.
Answer
\[ \boxed{(A-B)\cap(B-A)} \]
Correct option: (a)
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