Question

A relation R is defined on the set A = { 1,2,3,4,5,6 } by R = { ( x , y ) : y is divisible by x } .Verify whether R is symmetric and reflexive or not . Give reason ?

Answer 1

Given that $A=1,2,3,4,5,6$

$R=(x,y):yisdivisiblebyx$

We know that any number x is divisible by itself

$(x,x)\in R$

$\therefore$ R is reflexive

Now $(3,6)\in R$

Here 6 is divisible by 3

But $(6,3)\notin R$

Here $3$ is not divisible by $6$

$\therefore$ R is not symmetric

$\therefore$ R is reflexive but not symmetric