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 $(a \cup b)$:
$n(a \cup b) =$

Explanation:

Step1: Recall union count formula

The formula for the number of elements in the union of two sets is $n(A \cup B) = n(A) + n(B) - n(A \cap B)$

Step2: Count elements in set A

Count elements in $A=\{1,7,10,12,13,14,18\}$: $n(A)=7$

Step3: Count elements in set B

Count elements in $B=\{3,4,5,6,10,12,13,14,19,20\}$: $n(B)=10$

Step4: Find intersection $A\cap B$

Identify common elements: $A\cap B=\{10,12,13,14\}$, so $n(A\cap B)=4$

Step5: Calculate $n(A\cup B)$

Substitute values into formula: $n(A \cup B)=7+10-4$

Answer:

$13$