In problems 1-5 below, I will list a set S and a rule that defines a relation R
ID: 3734334 • Letter: I
Question
In problems 1-5 below, I will list a set S and a rule that defines a relation R on S as follows: (m, n) E R if m and n satisfy the given rule. For each set and rule, do the following six things: A. List the ordered pairs in the relation B. Draw the associated digraph. C. Give the matrix representation of the relation. Be sure to label the rows and columns with the elements of S. (If S is infinite, only include the subset of S that is actually used in the relation.) Identify which properties the relation has: reflexive, antireflexive, or neither; symmetric, antisymmetric, or neither, transitive or not transitive D. E. Decide whether the relation is an equivalence relation. If so, identify the equivalence classes F. Discuss whether the relation is a function or not. 2. S [0,1,2]; m-maxfn, 1). 3. S-[4,9,17); m zn. 4. S = {0,2,5); mn = 0. s. s-(1.26,7,.11:3(-B-o 0.Explanation / Answer
A.1) Ordered pair (m,n) is a pair of object.The ordered pair(m,n) is different from ordered pair(n,m). Set S contains all natural numbers where S=N means N={1,2,3....}. The set S contains two element which is defined as (m,n) and they are belong to relation R.
From problem 1 it defines that the sum of two ordered pair object must be equal to 5.
List of ordered pair in the relation R for S={1,2,3,4} and which can be represented in this way {(1,2),(1,3),(1,4),(2,3),(3,4)} but for m+n=5 we have to chose only two set of values {(1,4),(2,3)}
A.2) S={0,1,2}; where m=max{n,1}
m and n also contain elements{0,1,2} so when we find the m=max{0,1},m=max{1,1},m=max{2,1} result contain in m={1,2} and repetation can not present in set
A.3) S={4,9,17} represented as {(4,4),(4,9),(4,17),(9,4),(9,9),(9,17),(17,4),(17,9),(17,17)}
m>=n represent the are {(4,4),(9,4),(9,9),(17,4),(17,9),(17,17)}
A.4) S={0,2,5} ; where mn=0 represent as {(0,2),(0,5),(2,0),(5,0)}
B.1. Associated Digraph is like
1 4
2 3
B.4) 0 0 2 0
2
5 5 0
C.1)
C.2)
C.3)
C.4)
D)1) It has no reflexive property.
D)2) It has a partial reflexive property.
D)3) It has total reflexive property. Because its shows relation for m tends to m in relatiom.
D)4) Again it has aprtial reflexive property.
Rows (1,2) (1,3) (1,4) (2,3) (3,4) R1(m+n=5) No No Yes Yes No