Question

let ( u = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ), ( a = {1, 3, 5, 7, 9} ), ( b = {2, 4, 6, 8, 10} ), and ( c = {2, 3, 6, 7, 8, 9} ). list the elements of each set. (enter your answers using roster notation. enter empty or ( varnothing ) for the empty set.)
(a) ( a^c )
( varnothing )
(b) ( b cup c )

(c) ( c cup c^c )

Explanation:

Step1: Find complement of A

$A^C = U - A = \{1,2,3,4,5,6,7,8,9,10\} - \{1,3,5,7,9\} = \{2,4,6,8,10\}$

Step2: Find union of B and C

$B \cup C = \{2,4,6,8,10\} \cup \{2,3,6,7,8,9\} = \{2,3,4,6,7,8,9,10\}$

Step3: Find complement of C, then union with C

$C^C = U - C = \{1,2,3,4,5,6,7,8,9,10\} - \{2,3,6,7,8,9\} = \{1,4,5,10\}$
$C \cup C^C = \{2,3,6,7,8,9\} \cup \{1,4,5,10\} = \{1,2,3,4,5,6,7,8,9,10\}$

Answer:

(a) $\{2, 4, 6, 8, 10\}$
(b) $\{2, 3, 4, 6, 7, 8, 9, 10\}$
(c) $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$