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) − Cand A − (B − C).(Enter your answer in set-roster notation.) (A − B) − C A − (B − C) Are these sets equal? Yes No

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

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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