Question

(1) [6pts] Let R be the relation {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0)} defined on the set {0, 1, 2, 3}. Find the following: 1. [3pts] Reflexive closure of R 2. [3pts] Symmetric closure of R

Answer 1

Following are the solution to the given points:

Explanation:

In point 1:

The Reflexive closure:

Relationship R reflexive closure becomes achieved with both the addition(a,a) to R Therefore, (a,a) is
`(0,0),(1,1),(2,2) \ and \ (3,3)`

Thus, the reflexive closure:
`R={(0,0),(0,1),(1,1),(1,2),(2,0),(2,2),(3,0), (3,3)}`

In point 2:

The Symmetric closure:

R relation symmetrically closes by adding(b,a) to R for each (a,b) of R Therefore, here (b,a) is:
`(0,1),(0,2)\ and \ (0,3)`

Thus, the Symmetrical closure:

`R={(0,1),(0,2),(0,3)(1,0),(1,1)(1,2),(2,0),(2,2),(3,0), (3,3)}`