Unformatted text preview: 1 and itself). Prove that √ p is irrational. 2 4. Prove the following assertion by contraposition: if x is irrational, then x + r is irrational for all rational numbers r . (For guidance, see note 391 on page A19 at the end of Appendix A in the textbook). 5. Every prime number greater than 2 is odd. Is the converse true? 6. Prove that there are inﬁnitely many prime numbers. (Use proof by contradiction; for guidance, see note 390 on page A19 at the end of Appendix A in the textbook). 1 “disprove” means to prove the negation of the claim, which in this case is the assertion that not all natural numbers that are divisible by 6 and 8 are divisible by 48. 2 You may use the following known fact about prime numbers: if p is a prime number and a,b are integers such that a · b is divisible by p , then either a is divisible by p or b is divisible by p ). 1...
View
Full Document
 Winter '11
 Wiley
 Differential Equations, Calculus, Equations

Click to edit the document details