Question

for the universal set, ( u = {4, 5, 6, 7, 8, 9} ), complete the parts below. write your answers in roster form or as ( varnothing ). (a) suppose ( b = {4, 7, 8} ). then what is ( b )? ( b = square ) (b) suppose we know that ( c = {6, 7, 8, 9} ). then what would ( c ) have to be? ( c = square )

Explanation:

Step1: Find complement of set B

The complement \(B'\) is all elements in universal set \(U = \{4, 5, 6, 7, 8, 9\}\) not in \(B = \{4, 7, 8\}\).
\(B' = U - B = \{5, 6, 9\}\)

Step2: Find set C from its complement

Set \(C\) is all elements in \(U\) not in \(C' = \{6, 7, 8, 9\}\).
\(C = U - C' = \{4, 5\}\)

Answer:

(a) \(B' = \{5, 6, 9\}\)
(b) \(C = \{4, 5\}\)