10. Given an example of a relation. Which is

(i) Symmetric but neither reflexive nor transitive.

(ii) Transitive but neither reflexive nor symmetric.

(iii) Reflexive and symmetric but not transitive.

(iv) Reflexive and transitive but not symmetric.

(v) Symmetric and transitive but not reflexive.

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Answered by

Vishal Baghel | Contributor-Level 10

9 months ago

Let A= ${a, b, c}$

(i) R= ${(a, b), (b, a)}$ is a relation in set A

So, $(a, b) \in R$ and $(b, a) \in R \to$ Symmetric

$(a, a) \notin R \to$ not reflexive

$(a, b) \in R, (b, a) \in R$ but $(a, a) \notin R$ $\to$ not transitive

(ii) R= ${(a, b), (b, c), (a, c)}$ is a relation in set A

So, $(a, a) \notin R \to$ not reflexive

$(a, b) \in R$ but $(b, a) \notin R \to$ not symmetric

$(a, b) \in R & (b, c) \in R$ and also $(a, c) \in R \to$ transitive

(iii) R= ${(a, a), (b, b), (c, c), (a, b), (b, a), (a, c), (c, a)}$

So, $(a, a), (b, b), (c, c) \in R \to$ Reflexive

$(a, b) \in R \to (b, a) \in R \to$ Symmetric

$(a, c) \in R \to (c, a) \in R$

$(b, a) \in R$ and $(a, c) \in R$

But $(b, c) \notin R \to$ not transitive

(iv) R= ${(a, a), (b, b), (c, c), (a, b), (b, c), (a, c)}$ is s relation in set A

So, $(a, a), (b, b), (c, c) \in R \to$ reflexive

$(a, b) & (b, c) \in R$ so, $(a, c) \in R \to$ transitive

$(a, b) \in R$ b

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