Question

let $s$ be the universal set, where:
$s = \\{1, 2, 3, ... , 28, 29, 30\\}$
let sets $a$ and $b$ be subsets of $s$, where:

set $a = \\{1, 3, 8, 14, 20, 24, 29, 30\\}$

set $b = \\{2, 8, 10, 13, 16, 19, 23\\}$

set $c = \\{6, 7, 12, 17, 18, 20, 22, 23, 24, 30\\}$

find the number of elements in the set $(a \cap c) \cap b^c$
$n(a \cap c) \cap b^c = $

you may want to draw a venn diagram to help answer this question.
question help: video 1 video 2

Explanation:

Step1: Find $A \cap C$

Identify common elements in $A$ and $C$:
$A = \{1, 3, 8, 14, 20, 24, 29, 30\}$, $C = \{6, 7, 12, 17, 18, 20, 22, 23, 24, 30\}$
$A \cap C = \{20, 24, 30\}$

Step2: Find $B^c$

Elements in $S$ not in $B$:
$S = \{1,2,3,...,30\}$, $B = \{2,8,10,13,16,19,23\}$
$B^c = \{1,3,4,5,6,7,9,11,12,14,15,17,18,20,21,22,24,25,26,27,28,29,30\}$

Step3: Find $(A \cap C) \cap B^c$

Identify common elements from Step1 and Step2:
$(A \cap C) \cap B^c = \{20, 24, 30\}$

Step4: Count elements in the set

Count the elements from Step3:
$n[(A \cap C) \cap B^c] = 3$

Answer:

3