First slide

Operations on Sets

Question

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

Moderate

A

5
B

30
C

10
D

4

Solution

$\begin{array}{l} A \cup B = {1, 2, 3, 4, 5}, n (A \cup B) = 5 \\ \begin{array}{ll} A \cap B & = {3, 4}, n (A \cap B) = 2 \\ A Δ B & = (A ~ B) \cup (B ~ A) = {1, 2} \cup {5} \\ = {1, 2, 5} \end{array} \end{array}$
$n (A Δ B) = 3$ Hence $\begin{array}{l} n ((A \cup B) \times (A \cap B) \times (A Δ B)} \\ = 5 \times 2 \times 3 = 30 \end{array}$

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