CMSC150 Homework 3 | Complete Solution

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: f(x;y)jxand yaresiblingsg.
2
Determine whether each function is one-to-one, onto, or both (check only one):(2 points, 1 point each)
1. g : ZZwhere g is defined by g(x) = x􀀀1
one-to-one: onto: both:
2. f : NNwhere f is defined by f (x) =
x2
i f x iseven
x+1 i f x isodd

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)