If $17\equiv 3\left(\text{ mod }7\right)$ , $9\equiv 2( \mathrm{mod} 7)$ , then among the following a correct statement is

i) $17+9\equiv 3+2\left(\text{ mod }7\right)$       ii) $17+7\equiv 9+7\left(\text{mod }7\right)$

iii) $17\times 9\equiv 3\times 2\left(\text{mod }7\right)$         iv) $17-9\equiv 3-2\left(\text{mod }7\right)$

By congruence modulo property ,

If $a_1\equiv b_1\left(\mathrm{mod}n\right)$ and $a_2\equiv b_2\left(\mathrm{mod}n\right)$

i)  $a_1\pm a_2\equiv b_1\pm b_2\left(\mathrm{mod}n\right)$

ii)  $a_1{a}_2\pm b_1{b}_2\left(\mathrm{mod}n\right)$

So to check

i) $17+9=3+2\left(\mathrm{mod}7\right)$

$17\equiv 3\left(\mathrm{mod}7\right)$  and  $9\equiv 2\left(\mathrm{mod}7\right)$

$7|17-3$ and $7|9-2$

$\therefore$ It’s clearly true.