In the year $2022,$ a certain Magazine surveyed the executive officers of $500$ largest manufacturing companies in Asia. Of these $500$ persons, $310$ had a degree $($of any sort$)$ in Engineering, $238$ had an undergraduate degree in Engineering, and $184$ had a postgraduate degree in Engineering. Using a Venn diagram or otherwise, determine

i$.$ How many executive officers had both undergraduate and post graduate degrees in Engineering?

ii$.$ How many executive officers had no undergraduate and no postgraduate degree in Engineering?

iii. How many executive officers had at most one degree?