If  A={$x\in Z^{+}$ :$x<10$  and x is a multiple of 3 or 4}, then

	List – I		List – II
I)	Number of relations from A to A	P)	25
II)	Number of symmetric relations on A	Q)	$2^{20}$
III)	Number of reflexive relations on A	R)	$2^{15}$
IV)	Number of elements in A x A	S)	$2^{25}$

$\mathrm{A}=\left\{n\in Z^{+}:x<10\text{ and }x\text{ is a multiple of }3\text{ or }4\right\}$

$\therefore A=\left\{3,4,6,8,9\right\}$

$n\left(A\right)=5=n$

I) No. of relations on A $=2^{n^2}=2^{25}$

II) No. of symmetric relations on A $=2^{\frac{n(n+1)}{2}}=2^{\frac{5\left(6\right)}{2}}=2^{15}$

III) No. of reflexive relations on A $=2^{n(n-1)}=2^{5\left(4\right)}=2^{20}$

IV) No. of elements on A x A $=n\left(A\right)\times n\left(A\right)=5\times 5=25$