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
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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 onetoone, onto, or both (check only one):(2 points, 1 point each)
1. g : Z×Zwhere g is defined by g(x) = x?1
onetoone: onto: both:
2. f : N×Nwhere f is defined by f(x) = x
2
i f xis even
x+1 i f xis odd
onetoone: 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 onetoone? Explain.
2. Is f onto? Explain.
4
1. List all the functions from the twoelement set {1,2} to the threeelement set {a,b,c}. (1 point)
2. Which functions, if any, are onetoone?(1 point)
3. Which functions, if any, are onto?(1 point)

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Solution: CMSC 150 Homework 3 Summer15 Solution