Part C and D 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 isyour 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.

Solution c: Given that A=2112 We can write it as A=212×16⇒A=21216⇒A=216 Since 2 is a irrational…

Answered: Show by a (short) direct proof that…

Show by a (short) direct proof that 2/12 is irrational. d. Use a disproof by counter-example to prove that the converse of b. is not true: False Claim. If /6 is irrational then r is also irrational.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter10: Inequalities

Section10.2: Solving Inequalities

Problem 62WE

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Question

Part C and D

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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