PLEASE EXPLAIN AND SHOW WORK IF YOU WANT TO RECEIVE POINTS Determine whether R i

Question

PLEASE EXPLAIN AND SHOW WORK IF YOU WANT TO RECEIVE POINTS

Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. Let A = {1, 2, 3,4} and R be a relation on the set A defined by R = {(1,2)}. Let A = {1, 2, 3,4} and R be a relation on the set A defined by: R = {(1,1), (2,2), (3,3), (1,2), (2,1), (1,4), (3,2), (3,1), (3,4), (4,2), (4,1)}. Let A = {1, 2, 3, 4, 5} and R be the relation on the set A whose digraph is: Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive.

Explanation / Answer

[1]

(A)

In order for a set to have the reflexive property all elements must be related to themselves. A has the elements {1,2,3,4} so we know that we need to have {(1,1),(2,2),(3,3),(4,4)} those pairs at least for the set to be reflexive. Checking R, we see that this is not true.

opposite to this relation is irreflexive so A is irreflexive

In order for a set to have the symmetric property if an elements relates to another element, that element must also relate back to the original element. In our case this means if we have (1,2) - meaning 1 relates to 2, we know that somewhere in the set we must also have (2,1) - 2 relating back to 1. If that second pair is not in the set, then we know this does not have the symmetric property. Checking R for this, we see that it does not have this property. 1 relates to 2 and 2 does not relate back to one

opposite to this relation is anti symetric so A is anti symmetric

A set is said to have the transitive property if it has elements such that element a relates to element b and element b relates to element c, then element a must also relate to c. In our case we have only one so not transitive

(B)

similarly

R has {(1,1),(2,2),(3,3),(4,4)} so relation is reflexive

there is (3,2),(3,4),(3,1),(4,2) but no (2,3),(4,3),(1,3),(2,4)

so anti symmetric

it has (1,2) ,(2,1) and (1,1)

and (1,4),(4,1) and (1,1) and others so transitive

[2]

here R has { (2,2),(1,2),(2,5),(4,5),(1,4),(2,3) }

so there is no (1,1) so irreflexive

there is (1,2) but no (2,1) so anti symmetric

there is (1,2) and (2,3) but no (1,3) so not transitive

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.