4130sols1 - 4130 HOMEWORK 1 Due Thursday February 4 (1)...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
4130 HOMEWORK 1 Due Thursday February 4 (1) Section 1.1.3 Exercise 2b. “The only even prime is 2.” There are many different ways of approaching the problem. One way is n N ( n is even n is prime = n = 2) . The negation is n N ( n is even n is prime n 6 = 2) . That is, “There exists an even prime which is not equal to 2.” (2) Section 1.1.3 Exercise 3b. “Every nonzero rational number has a rational reciprocal.” x Q \ { 0 }∃ y Q ( xy = 1) . The corresponding statement with quantifiers reversed is: y Q x Q \ { 0 } ( xy = 1) . This is false, because if y Q is such that yx = 1 for all x Q \ { 0 } then y = 2 y = 1 which is impossible. (3) Let A be a set and let P ( a ) be a statement about an element of a . We write ! a AP ( a ) for “there exists a unique a A such that P ( a )”. (a) Write the statement ! a AP ( a ) in a form which uses the quantifiers and , and no connec- tives apart from
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

4130sols1 - 4130 HOMEWORK 1 Due Thursday February 4 (1)...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online