Question

If $A=\{1,2,3,4\},B=\{3,4,5\}$ then the number of elements in $(A\cup B)\times (A\cap B)\times (A\Delta B)$ is

• A. 5
• B. 30
• C. 10
• D. 4

Answer 1

Answer: (B)

$A\cup B=\{1,2,3,4,5\}.n(A\cup B)=5$
$A\cap B=\{3,4\},n(A\cap B)=2$
$A\Delta B=(A\sim B)\cup (B\sim A)=\{1,2\}\cup \{5\}$
$=\{1,2,5\}$
$n(A\Delta B)=3.\text{ Hence }n((A\cup B)\times (A\cap B)\times (A\Delta B)\}$
$=5\times 2\times 3=30.$