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\\}"
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