Non-reflexive, symmetric, transitive binary relation

Question

Non-reflexive, symmetric, transitive binary relation

Give an example of a binary relation R ⊂ A × A, where A = {a, b, c,d, e}, which is non-reflexive, symmetric, transitive, and construct its matrix.

1

дискретная-математика

Author: Bohdan, 2020-10-27

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1 answers

score 1 · Accepted Answer

Give an example of a binary relation R ⊂ A × A, where A = {a, b, c,d, e}, which is antireflexive, symmetric, transitive

An empty relation.

 R = ∅ ⊆ A × A

Construct its matrix.

 R | a | b | c | d | e
---|---|---|---|---|---
 a | 0 | 0 | 0 | 0 | 0
 b | 0 | 0 | 0 | 0 | 0
 c | 0 | 0 | 0 | 0 | 0
 d | 0 | 0 | 0 | 0 | 0
 e | 0 | 0 | 0 | 0 | 0