These are the logical symbolic arguments. What kind of rules these arguments involve porove them with the help of logical rules such as Implication rule, conjunction rule, Modus Tollens rule and so on.

(x) [(Ix =>Ax)] (x) [(PX ^ IX)] :. (3x) [(Px ^ Ax) ] (x) [(Mx => Nx) ] (3x) [(Mx ~ Ox) ] .: (3x)[ (Nx ^ Ox)] (x) [(Dx => Cx)] (3x)[(Ax ^ Dx)I : (3x)[(Ax ^ Cx)] ( x) [(PX => Qx)] (3x) [(RX ^ Px)] : (x) [(RX ^ Qx)] ( x) [( TX => Ux)] - Ut .. -Tt