$(1+1=2pts$ A "reset$-$dominant flip$-$flop" behaves like an S$-$R flip$-$flop, except that the input $S=R=1$ is allowed and the flip$-$flop is reset to $0$ when $S=R=1$

$($a$)$ Show the state table, construct the K$-$map and derive the characteristic equation for a reset$-$dominant flip$-$flop.

$($b$)$ Show how a reset$-$dominant flip$-$flop can be constructed by adding gate$($s$)$ to an S$-$R flip$-$flop.