Questions $2$a and $2$b are about the backtracking procedure MAKE$-$SETS and its helper MAKING$-$SETS, written in Cormen$$s pseudocode. The symbol $$ is the empty set, and the symbol $$ is the set union operator. The parameters n$,$ k$,$ and e are nonnegative integers. The parameter s is a set of nonnegative integers.

MAKE$-$SETS$($n$,$k$)$

$$MAKING$-$SETS$($n$,$k$,1,)$

$$

MAKING$-$SETS$($n$,$k$,$e$,$s$)$

$$if$$k$==0$

$$print$$s$$

$$else$$

$$for$$e$=$e$$to$$n$$

$$MAKING$-$SETS$($n$,$k$1,$e$+1,$s$\{$e$\})$

$2$a$.(5$ points.$)$ What will MAKE$-$SETS$(4,3)$ print? Hint: enumerate calls to MAKING$-$SETS breadth$-$first.

$2$b$.(5$ points.$)$ Suppose that n and k are nonnegative integers. What does MAKE$-$SETS$($n$,$k$)$ compute? Your answer must be one short sentence, stated in terms of n and k$.$