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 = {1, 2, 4, 5, 8, 9}. List the elements of each set.

Answer 1

Answer:

$C\ n\ C^c = \{ \}$

$(A\ n\ C)^c = \{2,3,4,6,7,8,10\}$

$A\ u\ (B\ n\ C) = \{1, 2,3, 4,5, 7, 8,9\}$

Step-by-step explanation:

Required

Determine

$C\ n\ C^c$

$(A\ n\ C)^c$

$A\ u\ (B\ n\ C)$

Solving $C\ n\ C^c$

$C^c$ implies that elements in U but not in C

Since

$C = \{1, 2, 4, 5, 8, 9\}$

$C^c = \{3, 6, 7, 10\}$

$C\ n\ C^c = \{1, 2, 4, 5, 8, 9\}\ n\ \{3, 6, 7, 10\}$

$C\ n\ C^c = \{ \}$

Because there's no intersection between both

Solving $(A\ n\ C)^c$

First, we need to determine A n C

$A\ n\ C = \{1, 3, 5, 7, 9\}\ n\ \{1, 2, 4, 5, 8, 9\}$

$A\ n\ C = \{1, 5, 9\}$

$(A\ n\ C)^c = (\{1, 5, 9\})^c$

$(A\ n\ C)^c = \{2,3,4,6,7,8,10\}$

Solving $A\ u\ (B\ n\ C)$

First, we need to determine B n C

$B\ n\ C = \{2, 4, 6, 8, 10\}\ n\ \{1, 2, 4, 5, 8, 9\}$

$B\ n\ C = \{2, 4, 8\}$

So:

$A\ u\ (B\ n\ C) = \{1, 3, 5, 7, 9\}\ u\ \{2,4,8\}$

$A\ u\ (B\ n\ C) = \{1, 2,3, 4,5, 7, 8,9\}$