Answer to Question #309514 in Discrete Mathematics for Showi

Question

.4 If Universal Set U = {90, 91 , 92 , 93 , 94, 95 , 96 , 97 , 98, 99 , 100} (10)

A = {90, 92, 94, 96, 98, 100}, B= {91, 93, 95, 97, 99},

C = {90, 94, 98}

1.4.1 What is (A ∩ C)c 1.4.2 What is (B ∪ C

give steps please

Answer 1

Let

$U = \{90, 91 , 92 , 93 , 94, 95 , 96 , 97 , 98, 99 , 100\}$

$A =\{90, 92, 94, 96, 98, 100\}, B= \{91, 93, 95, 97, 99\},\ C = \{90, 94, 98\}.$

Then

$(A ∩ C)^c =(\{90, 92, 94, 96, 98, 100\}\cap \{90, 94, 98\})^c=\{90, 94, 98\}^c \\= \{ 91 , 92 , 93 , 95 , 96 , 97 , 99 , 100\}.$

$B ∪ C= \{91, 93, 95, 97, 99\}\cup \{90, 94, 98\}=\{90,91, 93,94,95, 97, 98,99\}.$