Let A = 1, 2, 3, 4, 5 and R be a relation defined by R = ( x, y ) :...

We first write the elements of the set $R$.

i.e. $R = { (1,4) , (4,1) , (2,3) , (3,2) }$

Since, $(1,1) \notin R ⇒ R$ is not reflexive.

Now as,$(1,4) \in \mathbb{R} ⇒ (4,1) \in \mathbb{R}$ and $(2,3) \in \mathbb{R}$

$⇒ (3,2) \in \mathbb{R}$

So, $R$ is symmetric

Now, $(1,4) \in \mathbb{R}$ and $(4,1) \in \mathbb{R}$

Thus, $R$ is not transitive.

Hence, $R$ is symmetric but neither reflexive nor transitive.