$($c$)(1$ point$)$ Write down the type of

let rec f x y $=$ if x then $\{$ f y$,$ y $\}$ else $\{$ y$,$ f x $\}$

If you believe typing checking this function fails with "mismatched types", write "mis$-$ matched types". If you believe this function should trigger the occurs$-$check exception in our type inference algorithm in Assignment $5,$ write "occurs$-$check exception".