$(10\%)$Analyze the latch circuit shown.

$($a$)$ Derive the next$-$state equation for this circuit using Q as the state variable and P as an output.

$($b$)$ Construct the state table and output table for the circuit. Circle the stable states of the circuit.

$($c$)$ Are there any restrictions on the allowable input combinations on A and B$?$ Explain your answer.

Please answer all three questions