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: (g) ACN BCo fre R|-3 < x < 2}o fr€R|xs -3 or x > 2}o fre R|-3 s *s 2}o fre R/x « -2 orx 2 3}(h) AC U BC-1o fre R|-15x=0}o {re R]x < -1 or x 2 0}o fre R|-1 < * * 0}o fre Rx su or x > 1}(i) (AN B)Co fre R|-1 < ** a}o fxe R/x s u or x » 1}o{xe R]xs -1 or x > o}o fre R|-1 2}o fre R|-3sx < 2}o fre R/x< -2 or x 2 3} (d) AUC-3 < xofre R|-3 2}o fre R|-1 5xs 2}ofre R|-1

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Answered: Let the universal set be ℝ, the set of…

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:

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:

(g) ACN BC
o fre R|-3 < x < 2}
o fr€R|xs -3 or x > 2}
o fre R|-3 s *s 2}
o fre R/x « -2 orx 2 3}
(h) AC U BC
-1
o fre R|-15x=0}
o {re R]x < -1 or x 2 0}
o fre R|-1 < * * 0}
o fre Rx su or x > 1}
(i) (AN B)C
o fre R|-1 < ** a}
o fxe R/x s u or x » 1}
o{xe R]xs -1 or x > o}
o fre R|-1 <x < 0}
(i) (A U B)C
이ERI-J<x <가}
o {r€Rx < -3 or x 2 2}
o {xe R/xs -3 or x > 2}
o fre R|-3sx < 2}
o fre R/x< -2 or x 2 3}

(d) AUC
-3 < x
ofre R|-3 <x< 0 or 5 < xs 7}
o fre R|-3 5xs0or 5 <x<7}
|-3 SxS0or5 <x< 가}
o {xeR-3 s xs 0 and 5 < x s 7}
|(e) AnC
o {xeR|-3 s x s 0 or 5 < x s 7}
o {reR|-3 <x< 0 or 5 <xs 7}
o {x€R|-3 5 x s 0 or 5 < x< 7}
< :
o {xeR -3 s x s 0 and 5 < xs 7}
|(f) BC
o fre R/x< -1 or x > 2}
o fre R|-1 5xs 2}
ofre R|-1 <x< 2}
o {re R/xs -1 orx22}
o {re R/xs -2 0r x 2 1}

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