Answer:
a) [tex]B \cup C'=\{1,3,5,7,8\}[/tex]
b) [tex](B \cup C)'=\{5\}[/tex]
Problem:
U={1, 2, 3, 5, 7, 8)
B={1, 3, 7,8)
C={1,2}
Find the following sets.
Write your answer in roster form or as Ø.
(a) BUC' =
(b) (BUC)' =
Step-by-step explanation:
a)
We will need to find [tex]C'[/tex].
[tex]C'[/tex] is the elements in the universe [tex]U[/tex] that aren't in [tex]C[/tex].
[tex]U=\{1,2,3,5,7,8\}[/tex]
[tex]C=\{1,2\}[/tex]
So [tex]C'=\{3,5,7,8\}[/tex].
[tex]B \cup C'[/tex]
[tex]\{1,3,7,8\} \cup\{3,5,7,8\}[/tex]
union means it is in either/or so we have:
[tex]\{1,3,5,7,8\}[/tex]
b)
We need to find [tex]B\cup C[/tex] first.
[tex]B\cup C[/tex]
[tex]\{1,3,7,8\}\cup \{1,2\}[/tex]
[tex]\{1,2,3,7,8\}[/tex]
So now [tex](B \cup C)'[/tex] means we are going to have the elements in the universe that aren't in [tex]B \cup C[/tex]:
[tex]U=\{1,2,3,5,7,8\}[/tex]
[tex]B\cup C=\{1,2,3,7,8\}[/tex]
[tex](B \cup C)'=\{5\}[/tex]
