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.

 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,

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