Question

let $s$ be the universal set, where:
$s = \\{1, 2, 3, ... , 18, 19, 20\\}$
let sets $a$ and $b$ be subsets of $s$, where:

set $a = \\{1, 7, 10, 12, 13, 14, 18\\}$

set $b = \\{3, 4, 5, 6, 10, 12, 13, 14, 19, 20\\}$

find the following:
the number of elements in the set $(a \cup b)$:
$n(a \cup b) = $
the number of elements in the set $(a \cap b)$:
$n(a \cap b)$ is
you may want to draw a venn diagram to help answer this question.

Explanation:

Step1: Identify elements in $A\cap B$

Find common elements of $A$ and $B$: $\{10,12,13,14\}$

Step2: Calculate $n(A\cap B)$

Count elements in the intersection: $n(A\cap B)=4$

Step3: Get $n(A)$ and $n(B)$

Count elements: $n(A)=7$, $n(B)=9$

Step4: Apply union formula

Use $n(A\cup B)=n(A)+n(B)-n(A\cap B)$

$$\begin{align*} n(A\cup B)&=7+9-4\\ &=12 \end{align*}$$

Answer:

$n(A\cup B)=12$
$n(A\cap B)=4$