GO Classes Set Theory And Algebra Practice Set 1 | Question: 10

Question

Are the following relations reflexive, symmetric, transitive, antisymmetric? Explain.

• A. Let $R$ be a relation on $\mathbb{Z}$ such that $(a, b) \in R$ iff $b=a$ or $b=-a$.
• B. Let $R$ be a relation on $\mathbb{R}$ such that $(a, b) \in R$ iff $a b \leq 0$.
• C. Let $R$ be a relation on $\mathbb{R}$ such that $(a, b) \in R$ iff $a+2 b=17$.
• D. Let $R$ be a relation on $\mathbb{R}$ such that $(a, b) \in R$ iff $a+b$ is a rational number, that is can be represented by a fraction.

Answer 1

Ans-a) Reflexive, symmetric, transitive

Ans-b) Not reflexive, symmetric, not transitive

Ans-c) Not reflexive, not symmetric, not transitive

Ans-d) Reflexive, symmetric, transitive