Question

Let$A=3,5$ and $B=7,11$. Let $R=(a,b):a\in A,b\in B,a-bisodd$. Show that R is an empty relation form A into B.

Answer 1

$A=\{3,5\}$ $B=\{7,11\}$

$R=(a,b):a\in A,b\in B,a-b$ is odd.

Let $B=7,a=3$

$b-a=4,$ which is even.

Each element of $B$ is odd & $A$ also has odd elements.

Hence $a-b$ is never be odd, it will always negetive even no.

Hence $R=(a,b)\in \varphi$.