Let the universal set be ℝ, the set of all real numbers, and let A = {x ℝ | −3 ≤ x ≤ 0}, B = {x ℝ −1 < x < 2}, and C = {x ℝ | 5 < x ≤ 7}. Find each of the following: (a) A ∪ B x ℝ −3 ≤ x < 2 x ℝ −3 < x ≤ 2 x ℝ x ≤ −3 or x > 2 x ℝ x < −3 or x ≥ 2 ∅ (b) A ∩ B x ℝ −1 ≤ x < 0 x ℝ −1 < x ≤ 0 x ℝ x < −1 or x ≥ 0 x ℝ x ≤ −1 or x > 0 ∅ (c) Ac x ℝ −3 < x < 0 x ℝ −3 ≤ x ≤ 0 x ℝ x ≤ −3 or x ≥ 0 x ℝ x < −3 or x > 0 ∅
Let the universal set be ℝ, the set of all real numbers, and let A = {x ℝ | −3 ≤ x ≤ 0}, B = {x ℝ −1 < x < 2}, and C = {x ℝ | 5 < x ≤ 7}. Find each of the following: (a) A ∪ B x ℝ −3 ≤ x < 2 x ℝ −3 < x ≤ 2 x ℝ x ≤ −3 or x > 2 x ℝ x < −3 or x ≥ 2 ∅ (b) A ∩ B x ℝ −1 ≤ x < 0 x ℝ −1 < x ≤ 0 x ℝ x < −1 or x ≥ 0 x ℝ x ≤ −1 or x > 0 ∅ (c) Ac x ℝ −3 < x < 0 x ℝ −3 ≤ x ≤ 0 x ℝ x ≤ −3 or x ≥ 0 x ℝ x < −3 or x > 0 ∅
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 the universal set be ℝ, the set of all real numbers, and let
A = {x ℝ | −3 ≤ x ≤ 0},
B = {x ℝ −1 < x < 2},
and
C = {x ℝ | 5 < x ≤ 7}.
Find each of the following:(a)
A ∪ B
(b)
A ∩ B
(c)
Ac
(d)
A ∪ C
(e)
A ∩ C
(f)
Bc
(g)
Ac ∩ Bc
(h)
Ac ∪ Bc
(i)
(A ∩ B)c
(j)
(A ∪ B)c
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