For each of the following arguments, use the STTT to determine whether the argument is valid or invalid. For some of these arguments, Steps 2 C , 3 C , and 4 (i.e., the C-Sequence) will be most efficient; for some of these arguments Steps 2 P , 3 P , and 4 (i.e., the P-Sequence) will be most efficient.

(P₁): (S ⊃ T) ⋅ (T ⊃ S)
(P₂): (U ⋅ T)  (~ T ⋅ ~ U)
(P₃): (U ꓦ V) ꓦ (S ꓦ T)
(P₄): ~ U ⊃ (W ⋅ X)
(P₅): (V ⊃ ~ S) ⋅ (~ V ⊃ ~ Y)
(P₆): X . (~ Y ⊃ ~ X)
(P₇): (U ꓦ S) ⋅ (V ꓦ Z)
∴ X ⋅ Z