Let R be a relation on E. Demonstrate that: R is reflexive if and only if IdE subseteq R; R is symmetric only and only if R=R^{-1}.

Dawson Downs

Dawson Downs

Answered question

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

Beginner2022-07-17Added 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

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Discrete math

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?