Question

Let $R = \\{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\\}$ be a relation on the set $A = \\{1, 2, 3, 4\\}$. The relation R is

• A. a function
• B. transitive
• C. not symmetric
• D. reflexive

Answer 1

Answer: (C)

not symmetric

Answer 2

Let $R = \\{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\\}$ be a relation on the set $A = \\{1, 2, 3, 4\\}$.

Then

(a) Since $(2, 4) \in R$ and $(2, 3) \in R\:\: \therefore R$ is not a function

(b) Since $(1, 3) \in R$ and $(3, 1) \in R$ but $(1, 1) \therefore R \:\:$is not transitive.

(c) Since $(2, 3) \in R$ but $(3, 2) \notin\,R\,\therefore R$ is not symmetric.

(d) Since $(4, 4) \notin R \therefore R$ is not reflexive

$\therefore$ $R$ not symmetric holds.

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