Determine whether Relation `R` on the set `A={1,\ 2,\ 3,\ 4,\ 5,\ 6}` defined as `R={(x ,\ y): y` is divisible by `x}` is reflexive, symmetric or transitive.

Explanation

`A={1,2,3,4,5,6}`

R`={(x,y):y `is divisible by `x}`

We know that any number `(x) `is divisible by itself.

`(x,x)∈`R

\therefore R is reflexive.

Now,`(2,4)∈`R [as` 4` is divisible by `2`]

But,`(4,2) \!in` R. [as `2` is not divisible by` 4`]

\therefore R is not symmetric.

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