Equal[
  BooleanTable[Implies[p, q || r], {p, q, r}],
  BooleanTable[Implies[p && Not[q], r], {p, q, r}]
]

(* ==> True *)

Reduce[Equivalent[Implies[p, q || r], Implies[p && Not[q], r]]]

(* ==> True *)

tableFormattor[rawData_] := Insert[Insert[
Grid[rawData /. {0 -> 0,
   1 -> Item[1, Background -> Lighter[Magenta]]},
 FrameStyle -> Gray,
 Frame -> All], {Background -> {None, {GrayLevel[0.7], {White}}},
 Dividers -> {Black, {2 -> Black}}, Frame -> True,
 Spacings -> {2, {2, {0.7}, 2}}}, 2], {Dividers -> All,
Spacings -> .7 {1, 1}}, 2];


truthTable[f__] :=  Module[{}, atoms = Cases[Most[{f}],
 (a_ /;Length[a] == 0 [And] Not[StringQ[a]])];heads =
 ToString[TraditionalForm@#] & /@ {f};
  rawData = Transpose@Boole[BooleanTable[#, atoms] & /@ {f}];
  If[Last[{f}] === 1,
   Transpose@Boole[BooleanTable[#, atoms] & /@ Most[{f}]],
    If[Last[{f}] === "rev",
    truthTableFormattor[{ToString[
       TraditionalForm@#] & /@ (Most@{f})}~Join~
      Transpose[(Reverse /@
      Boole[BooleanTable[#, atoms] & /@ (Most@{f})])]],
     truthTableFormattor[{heads}~Join~rawData]]]];


truthTable[p, q, r, p [Implies] (q [Or] r), (p [And] [Not] q) [Implies] r]