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Let
A = {a, b, c},
B = {b, c, d},
and
C = {b, c, e}.
(a)
Find
A ∪ (B ∩ C),
(A ∪ B) ∩ C,
and
(A ∪ B) ∩ (A ∪ C).
(Enter your answer in set-roster notation.)
A ∪ (B ∩ C)
(A ∪ B) ∩ C
(A ∪ B) ∩ (A ∪ C)
Which of these sets are equal?
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
A ∪ (B ∩ C) = (A ∪ B) ∩ C = (A ∪ B) ∩ (A ∪ C)
(A ∪ B) ∩ C = (A ∪ B) ∩ (A ∪ C)
A ∪ (B ∩ C) = (A ∪ B) ∩ C
(b)
Find
A ∩ (B ∪ C),
(A ∩ B) ∪ C,
and
(A ∩ B) ∪ (A ∩ C).
(Enter your answer in set-roster notation.)
A ∩ (B ∪ C)
(A ∩ B) ∪ C
(A ∩ B) ∪ (A ∩ C)
Which of these sets are equal?
(A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C)
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
A ∩ (B ∪ C) = (A ∩ B) ∪ C
A ∩ (B ∪ C) = (A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C)
c)
Find
(A − B) − C
and
A − (B − C).
(Enter your answer in set-roster notation.)
(A − B) − C
A − (B − C)
Are these sets equal?
Yes
No
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