CMSC 150 Homework 3 Summer15

CMSC150

Introduction to Discrete Math

Summer 2015

Homework 3

June 3, 2015

The total number of points is 10. Your total score will be divided by 10 to produce a score over 100. Show all work

unless checkboxes are provided.

1

Decide whether each of the following relations is a function:(3 points, 1 point each)

1. The domain and codomain are {1,2,3,4,5} and the relation R is given by the set of ordered pairs:

{(1,5),(2,3),(3,3),(4,2),(5,1)}.

2. The domain and codomain are {1,2,3,4,5} and the relation R is given by the set of ordered pairs:

{(1,5),(2,3),(3,3),(1,2),(4,1)}.

3. The domain and codomain are the set of all people who were alive at midnight, December 31, 1999 and the

relation R is defined by the rule: {(x, y)|x and y are siblings}.

2

Determine whether each function is one-to-one, onto, or both (check only one):(2 points, 1 point each)

1. g : Z×Zwhere g is defined by g(x) = x?1

one-to-one: onto: both:

2. f : N×Nwhere f is defined by f(x) = x

2

i f xis even

x+1 i f xis odd

one-to-one: onto: both:

1

3

Let P be the power set of {a,b,c}. A function f: P ?Z, the set of integers, follows: For A in P, f(A)=the number of

elements in A.(2 points, 1 point each)

1. Is f one-to-one? Explain.

2. Is f onto? Explain.

4

1. List all the functions from the two-element set {1,2} to the three-element set {a,b,c}. (1 point)

2. Which functions, if any, are one-to-one?(1 point)

3. Which functions, if any, are onto?(1 point)