$A_{1}=\left \{ 1 \right \}$
$A_{2}=\left \{ 1,2 \right \}$
$A_{3}=\left \{ 1,2,3 \right \}$
Now, given that $|A_{i}|$ is odd number
So, value of $i$ is 1 or 3
Now we know , a set can contain even number of elements, if an odd number set is subtracted from another odd number set
or,
an even number set is subtracted from another even number set
Now, $||A_{i}|\cap|A_{j}| |=$even number
that means j value could be 1 or 3
Here n is largest number of that set
So, if n=3, m could be 1 or 3
So, $m\leq n$