Let A and B be sets. Use a proof by contradiction to show that An (B – A) = 0. your proof must be by contradiction. a. b. Let z be any positive real number. Use a proof by contradiction to show that if r is your proof must be by contradiction. irrational then r/6 is also irrational. Show by a (short) direct proof that 2/12 is irrational. с. d. Use a disproof by counter-example to prove that the converse of b. is not true: False Claim. If r/6 is irrational then r is also irrational.
Let A and B be sets. Use a proof by contradiction to show that An (B – A) = 0. your proof must be by contradiction. a. b. Let z be any positive real number. Use a proof by contradiction to show that if r is your proof must be by contradiction. irrational then r/6 is also irrational. Show by a (short) direct proof that 2/12 is irrational. с. d. Use a disproof by counter-example to prove that the converse of b. is not true: False Claim. If r/6 is irrational then r is also irrational.
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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Part B
Transcribed Image Text:Let A and B be sets. Use a proof by contradiction to show that An (B – A) = 0.
a.
your proof must be by contradiction.
b.
Let z be any positive real number. Use a proof by contradiction to show that if a is
your proof must be by contradiction.
irrational then r1/6 is also irrational.
Show by a (short) direct proof that 2/12 is irrational.
с.
d.
Use a disproof by counter-example to prove that the converse of b. is not true:
False Claim. If r/6 is irrational then r is also irrational.
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