$1.$ Design an MN Latch whose functionality is described with the below table.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash (\backslash$mathbf$\{$C t r l$\}\backslash )$ & $\backslash (\backslash$mathbf$\{$M$\}\backslash )$ & $\backslash (\backslash$mathbf$\{$N$\}\backslash )$ & $\backslash (\backslash$mathbf$\{$Q$\}\backslash )$ & $\backslash (\backslash$mathbf$\{$Q$\}^\{\backslash$prime$\}\backslash )$ & State $\backslash \backslash$

$\backslash$hline $0$ & $\backslash (\backslash$mathbf$\{$X$\}\backslash )$ & $\backslash (\backslash$mathbf$\{$X$\}\backslash )$ & $-$ & $-$ & No Change $\backslash \backslash$

$\backslash$hline $1$ & $0$ & $0$ & $0$ & $1$ & Reset $\backslash \backslash$

$\backslash$hline $1$ & $0$ & $1$ & $-$ & $-$ & toggle $\backslash \backslash$

$\backslash$hline $1$ & $1$ & $0$ & $-$ & $-$ & No change $\backslash \backslash$

$\backslash$hline $1$ & $1$ & $1$ & $1$ & $0$ & Set $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$