Let R be a relation on E. Demonstrate that:- R is reflexive if and only...

Dawson Downs

Dawson Downs

Answered

2022-07-16

Let R be a relation on E. Demonstrate that:
- R is reflexive if and only if I d E R;
- R is symmetric only and only if R = R 1.

Answer & Explanation

Abraham Norris

Abraham Norris

Expert

2022-07-17Added 16 answers

Step 1
Writing this kind of proof is mostly remembering the definitions. suppose R is a relation over A.for the first point, use the definition:
R is reflexive x A . < x , x >∈ R
and we have:
R  is reflexive x A . < x , x >∈ R { < x , x > | x A } R I d A R
Step 2
for the second one, we use the definition:
R is symmetric < x , y >∈ R . < y , x >∈ R
and so we get:
R is symmetric < x , y >∈ R . < y , x >∈ R { < y , x > | < x , y >∈ R } R R 1 R

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