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mote1985 [20]
3 years ago
5

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 element

s of each set.
Mathematics
1 answer:
Leto [7]3 years ago
4 0

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 = \{ \}

<em>Because there's no intersection between both</em>

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\}

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