Question

for the universal set, ( u = {1, 2, 3, 4, 5} ), complete the parts below. write your answers in roster form or as ( varnothing ). (a) suppose ( a = {2, 4} ). then what is ( a )? ( a = ) (b) suppose we know that ( b = {2, 3, 4, 5} ). then what would ( b ) have to be? ( b = )

Explanation:

Step1: Define complement of set A

The complement \(A^c\) contains all elements in \(U\) not in \(A\).
\(U = \{1, 2, 3, 4, 5\}\), \(A = \{2, 4\}\)

Step2: Calculate \(A^c\)

\(A^c = U - A = \{1, 3, 5\}\)

Step3: Define complement of set B

The set \(B\) contains all elements in \(U\) not in \(B^c\).
\(U = \{1, 2, 3, 4, 5\}\), \(B^c = \{2, 3, 4, 5\}\)

Step4: Calculate \(B\)

\(B = U - B^c = \{1\}\)

Answer:

(a) \(A^c = \{1, 3, 5\}\)
(b) \(B = \{1\}\)