Consider the following syllogisms, written in the symbolic language of predicate logic. Which one$($s$)$ are formally valid? $[$Hint: Convert to a form suitable to using Carroll diagrams.$]$

AAx$(Gx$notHx$),$EEx$(Hx$&$Ix)$:$.$AAx$(Gx$notIx$)$

AAx$(AxBx),$AAx$(BxDx)$:$.$AAx$(AxEx)$

EEx$(Sx$&$Tx),$EEx$(Tx$&$Rx)$:$.$EEx$(Sx$&$Rx)$

EEx$(Mx$&$Nx),$AAx$(MxOx)$:$.$EEx$(Nx$&$Ox)$

AAx$(Ax$notBx$),$AAx$(Bx$notCx$)$:$.$AAx$(Ax$notCx$)$