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.

Here,

A = {0,2,4,6,8,10}

B = {0,1,2,3,4,5,6}

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

So,

a) $A\cap B\cap C= \{4,6\}$

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

c)$(A\cup B)\cap C$

$A\cup B =\{0,1,2,3,4,5,6,8,10\}\\So,\ \ (A\cup B)\cap C=\{4,5,6,8,10\}$

d) $(A\cap B)\cup C$

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

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