hw02sol

# hw02sol - Math 55 Discrete Mathematics Fall 2008 Homework 2...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 55: Discrete Mathematics, Fall 2008 Homework 2 Solutions Problems marked * will be corrected fully, out of 10 points. The others will be checked quickly, for 2 points each. 2.3: 16. The following are not the only possible solutions but they are some of the simplest ones. (a) f ( n ) = n + 1. (b) f (0) = 0, f ( n ) = n- 1 if n > 0. (c) f (0) = 1, f (1) = 0, f ( n ) = n if n > 1. (d) f (0) = 1, f ( n ) = n if n > 0. 40. (a) f- 1 ( S ∪ T ) = { a ∈ A : f ( a ) ∈ S ∪ T } = { a ∈ A : f ( a ) ∈ S or f ( a ) ∈ T } = { a ∈ A : f ( a ) ∈ S } ∪ { a ∈ A : f ( a ) ∈ T } = f- 1 ( S ) ∪ f- 1 ( T ). (b) Just change ∪ to ∩ and “or” to “and” in the above solution to part (a). A more laborious but also correct way to do this is to verify in each part that the set on the left-hand side is a subset of the one on the right, and conversely. *[5 pts each part] (C) (i) It is true that if f ◦ g is one-to-one, then g is one-to-one. To prove it, suppose g ( x ) = g ( y ). Then f ◦ g ( x ) = f ◦ g ( y ), which implies x = y since f ◦ g is one-to-one. We have shown thatone-to-one....
View Full Document

## This note was uploaded on 08/16/2010 for the course MATH 55 taught by Professor Strain during the Fall '08 term at Berkeley.

### Page1 / 2

hw02sol - Math 55 Discrete Mathematics Fall 2008 Homework 2...

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

View Full Document
Ask a homework question - tutors are online