Question

Any subset of A × A is called a relation on the set A. A relation R on A is symmetric if
(a, b) ∈ R ⇒ (b, a) ∈ R ∀ a, b ∈ A. Give one example each, with justification, of
i) a symmetric relation on ,
ii) a relation that is not symmetric on the set {2, 3, 5, 7}.

Answer 1

Answer on Question #46918 – Math – Discrete Mathematics

Problem.

Any subset of $A \times A$ is called a relation on the set $A$. A relation $R$ on $A$ is symmetric if $(a, b) \in R \Rightarrow (b, a) \in R \ \forall a, b \in A$. Give one example each, with justification, of

i) a symmetric relation on,

ii) a relation that is not symmetric on the set $\{2, 3, 5, 7\}$.

Remark:

The statement is incorrectly formatted. Is suppose that correct statement is "Any subset of $A \times A$ is called a relation on the set $A$. A relation $R$ on $A$ is symmetric if $(a, b) \in R \Rightarrow (b, a) \in R \ \forall a, b \in A$. Give one example each, with justification, of

i) a symmetric relation on $\mathbb{N}$,

ii) a relation that is not symmetric on the set $\{2, 3, 5, 7\}$." (see http://ignou.ac.in/userfiles/MTE-04%20(E)%202014.pdf)

Solution:

i) The subset $R_i = \{(n, n) \in \mathbb{N} : n \in \mathbb{N}\}$ is a symmetric relation on $\mathbb{N}$, because if $(a, b) \in R_i$, then $a = b$ and $(a, a) = (b, a) \in R_i$.

ii) The subset $R_{ii} = \{(2,3), (3,5), (5,7)\}$ is not symmetric on the set, as $(2,3) \in R_{ii}$ and $(3,2) \notin R_{ii}$.

Answer: i) $R_i = \{(n, n) \in \mathbb{N} : n \in \mathbb{N}\}$, ii) $R_{ii} = \{(2, 3), (3, 5), (5, 7)\}$.

www.AssignmentExpert.com