Solution to Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, … - Sikademy
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Archangel Macsika

Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find a) A ∩ B ∩ C. b) A ∪ B ∪ C. c) (A ∪ B) ∩ C. d) (A ∩ B) ∪ C.

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Here's the Solution to this Question

 A = {0, 2, 4, 6, 8, 10}

 B = {0, 1, 2, 3, 4, 5, 6}

C = {4, 5, 6, 7, 8, 9, 10}

a.

A\cap B\cap C, requires us to determine the elements common to set A, set B and set C.

Therefore,

A\cap B\cap C=\{4,6\}


b.

A\cup B\cup C requires us to determine all elements in set A, B and C.

Therefore,

A\cup B\cup C=\{0,1,2,3,4,5,6,7,8,9,10\}


C.

(A\cup B)\cap C,

First, we need to determine (A\cup B), which are the elements in both set A and set B.

A\cup B=\{0,1,2,3,4,5,6,8,10\}.

Set C=\{4,5,6,7,8,9,10\}

Therefore, (A\cup B)\cap C requires us to determine elements common to (A\cup B) and set

C.

Hence,

(A\cup B)\cap C=\{4,5,6,8,10\}


d.

(A\cap B)\cup C

We first find elements common to set A and set B.

(A\cap B)=\{0,2,4,6\}

Set C=\{4,5,6,7,8,9,10\}

We now find all elements in the intersection(A\cap B) and set C.

Thus,

(A\cap B)\cup C=\{0,2,4,5,6,7,8,9,10\}.


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