Question

let ( s ) be the universal set, where:( s = {1, 2, 3, dots, 18, 19, 20} )let sets ( a ) and ( b ) be subsets of ( s ), where:set ( a = {2, 3, 8, 11, 12, 13, 14, 16} )set ( b = {2, 4, 5, 7, 9, 10, 14, 15, 16, 17} )find the following:list the elements in the set ( (a cup b) ):( (a cup b) = { } )enter the elements as a list, separated by commas. if the result is the empty set, enter dnelist the elements in the set ( (a cap b) ):( (a cap b) = { } )enter the elements as a list, separated by commas. if the result is the empty set, enter dneyou may want to draw a venn diagram to help answer this question.question help: video 1 video 2

Explanation:

Step1: Find union of A and B

Combine all unique elements from A and B.
$A \cup B = \{2,3,4,5,7,8,9,10,11,12,13,14,15,16,17\}$

Step2: Find intersection of A and B

Identify elements common to both A and B.
$A \cap B = \{2,14,16\}$

Answer:

$(A \cup B) = \{2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17\}$
$(A \cap B) = \{2, 14, 16\}$