Prove Induced matching is:

a$)$ NP

b$)$ NP hard, by writing the algorithmic steps using reduction from the following NP hard problems

Vertex cover

$-3$ sat

$-$clique

$-$Independent set

Prove hitting set is:

a$)N{P}_{?}$

b$)$ NP hard, by writing the algorithmic steps using reduction from the following NP hard problems

$-3$ sat

$-$independent set