Answer:
[tex]C\ n\ C^c = \{ \}[/tex]
[tex](A\ n\ C)^c = \{2,3,4,6,7,8,10\}[/tex]
[tex]A\ u\ (B\ n\ C) = \{1, 2,3, 4,5, 7, 8,9\}[/tex]
Step-by-step explanation:
Required
Determine
[tex]C\ n\ C^c[/tex]
[tex](A\ n\ C)^c[/tex]
[tex]A\ u\ (B\ n\ C)[/tex]
Solving [tex]C\ n\ C^c[/tex]
[tex]C^c[/tex] implies that elements in U but not in C
Since
[tex]C = \{1, 2, 4, 5, 8, 9\}[/tex]
[tex]C^c = \{3, 6, 7, 10\}[/tex]
[tex]C\ n\ C^c = \{1, 2, 4, 5, 8, 9\}\ n\ \{3, 6, 7, 10\}[/tex]
[tex]C\ n\ C^c = \{ \}[/tex]
Because there's no intersection between both
Solving [tex](A\ n\ C)^c[/tex]
First, we need to determine A n C
[tex]A\ n\ C = \{1, 3, 5, 7, 9\}\ n\ \{1, 2, 4, 5, 8, 9\}[/tex]
[tex]A\ n\ C = \{1, 5, 9\}[/tex]
[tex](A\ n\ C)^c = (\{1, 5, 9\})^c[/tex]
[tex](A\ n\ C)^c = \{2,3,4,6,7,8,10\}[/tex]
Solving [tex]A\ u\ (B\ n\ C)[/tex]
First, we need to determine B n C
[tex]B\ n\ C = \{2, 4, 6, 8, 10\}\ n\ \{1, 2, 4, 5, 8, 9\}[/tex]
[tex]B\ n\ C = \{2, 4, 8\}[/tex]
So:
[tex]A\ u\ (B\ n\ C) = \{1, 3, 5, 7, 9\}\ u\ \{2,4,8\}[/tex]
[tex]A\ u\ (B\ n\ C) = \{1, 2,3, 4,5, 7, 8,9\}[/tex]
