T$7.$ A new Flip$-$Flop is having behaviour as described below. It has two inputs $x$ and $Y$ and when both inputs are same and they are $1,1,$ the flip$-$flop is going to set else flip$-$flop resets. If both inputs are different and they are $0,1,$ filp$-$flop complements itsself otherwise it is going to retain the last state. Which of the following expression is the characteristic expression for the new flip flop?

$($a$)xQ+\frac{y}{b}ar(Q)$

$($b$)\frac{x}{b}ar(Q)+yQ$

$($c$)\frac{x}{b}ar(Q)+\frac{y}{b}ar(Q)$

$($d$)$ None