CMSC150 Homework 2 | Complete Solution

CMSC150 Introduction to Discrete Math Late Spring 2015 Homework 2

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
For the following binary relation R on N, decide which of the given ordered pairs belong to R:(1 point)
xRy$x + y < 7
(1,3),(2,5),(3,3),(4,4)
2
Let S={1,2,3}. Test the following binary relation for reflexivity, symmetry, antisymmetry, and transitivity.
R = {(1,1),(1,2),(2,3),(1,3)}(1 point)
Reflexivity:
Symmetry:
Antisymmetry:
Transitivity:
3
Let S be the set of people in the United States. Test the following binary relations on S for reflexivity, symmetry,
antisymmetry, and transitivity.
1
1. xRy $x is the same height as y(1 point)
Reflexivity:
Symmetry:
Antisymmetry:
Transitivity:
2. xRy $x is at least as tall as y(1 point)
Reflexivity:
Symmetry:
Antisymmetry:
Transitivity:
4
For the following binary relation on the given set S, list the set of ordered pairs of the relation (1 point) and test the
relation for reflexivity, symmetry, antisymmetry, and transitivity(1 point).
S={0,1,2,3,4,5}
xRy$x + y = 5
R={ }
Reflexivity:
Symmetry:
Antisymmetry:
Transitivity:
5
Let S = {0,1,2,4,6}. Find the reflexive, symmetric, and transitive closure of the following binary relation R:(1 point)
R={(0,1),(1,0),(2,4),(4,2),(4,6),(6,4)}
2
Reflexive closure:
Symmetric closure:
Transitive closure:
6
Given the partition {a,b,c} and {d,e} of the set S={a,b,c,d,e}, list the ordered pairs in the corresponding equivalence
relation.(1 point)
7
The notation [n] denotes an equivalence class.
For the equivalence relation R={(1,1),(2,2),(1,2),(2,1),(1,3),(3,1),(3,2),(2,3),(3,3),(4,4),(5,5),(4,5),(5,4)}
1. What is the set [4]? (1 point)
2. What is the set [3]?(1 point)
3