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.
, requires us to determine the elements common to set A, set B and set C.
Therefore,
b.
requires us to determine all elements in set A, B and C.
Therefore,
C.
,
First, we need to determine , which are the elements in both set A and set B.
.
Set
Therefore, requires us to determine elements common to and set
Hence,
d.
We first find elements common to set A and set B.
Set
We now find all elements in the intersection and set
Thus,
.