Proficiency #7. [Counterexamples] For each of the following two statements, give a counterexample to show that the state- ment is false. a. If r is an integer such that r = 1 mod 12, then r = 1 mod 12 or r = -1 mod 12. b. If A, B, D are sets such that AC B and B 4 D, then A 4 D.
Proficiency #7. [Counterexamples] For each of the following two statements, give a counterexample to show that the state- ment is false. a. If r is an integer such that r = 1 mod 12, then r = 1 mod 12 or r = -1 mod 12. b. If A, B, D are sets such that AC B and B 4 D, then A 4 D.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Proficiency #7. [Counterexamples]
For each of the following two statements, give a counterexample to show that the state-
ment is false.
a. If x is an integer such that x? = 1 mod 12, then x =1 mod 12 or x = -1 mod 12.
b. If A, B, D are sets such that A C B and B Z D, then A Z D.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ce9e3a3-dedc-4902-85ce-d3b117f9e3ef%2Fd09d1911-b42a-49b4-9406-275308e2ffe8%2Fl4vdze_processed.png&w=3840&q=75)
Transcribed Image Text:Proficiency #7. [Counterexamples]
For each of the following two statements, give a counterexample to show that the state-
ment is false.
a. If x is an integer such that x? = 1 mod 12, then x =1 mod 12 or x = -1 mod 12.
b. If A, B, D are sets such that A C B and B Z D, then A Z D.
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