Q.(e) If $A = \{1, 3, 5, 7, 9\}$, $B = \{1, 7, 8\}$ and $C = \{3, 5, 8, 10, 12\}$, then find $(A \cup B) \cap (B \cup C)$.

$A\triangle B=(A-B)\cup(B-A)$ — elements in exactly one of the two sets.

The symmetric difference of two sets $A$ and $B$ (denoted $A\triangle B$ or $A\ominus B$) is the set of all elements that belong to either $A$ or $B$ but not to both:

$A\triangle B=(A-B)\cup(B-A)=(A\cup B)-(A\cap B)$

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$A\cup B=\{11,12,13,14\}$, so $n(A\cup B)=4$.

List the union directly:

$A\cup B=\{11,12,13\}\cup\{12,13,14\}=\{11,12,13,14\}.$

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