AA

Solved 50

• PM ✱3·37 (Transp): $((p \land q) \supset r) \supset ((p \land {\sim} r) \supset {\sim} q)$Proved

  Oct 2026

• PM ✱5·24: ${\sim} ((p \land q) \lor ({\sim} p \land {\sim} q)) \equiv ((p \land {\sim} q) \lor (q \land {\sim} p))$Proved

  Oct 2026

• PM ✱5·33: $(p \land (q \supset r)) \equiv (p \land ((p \land q) \supset r))$Proved

  Oct 2026

• PM ✱5·61: $((p \lor q) \land {\sim} q) \equiv (p \land {\sim} q)$Proved

  Oct 2026

• PM ✱5·23: $(p \equiv q) \equiv ((p \land q) \lor ({\sim} p \land {\sim} q))$Proved

  Oct 2026

• PM ✱5·44: $(p \supset q) \supset ((p \supset r) \equiv (p \supset (q \land r)))$Proved

  Oct 2026

• PM ✱5·22: ${\sim} (p \equiv q) \equiv ((p \land {\sim} q) \lor (q \land {\sim} p))$Proved

  Oct 2026

• PM ✱5·32: $(p \supset (q \equiv r)) \equiv ((p \land q) \equiv (p \land r))$Proved

  Oct 2026

• PM ✱4·39: $((p \equiv r) \land (q \equiv s)) \supset ((p \lor q) \equiv (r \lor s))$Proved

  Oct 2026

• PM ✱4·38: $((p \equiv r) \land (q \equiv s)) \supset ((p \land q) \equiv (r \land s))$Proved

  Oct 2026

• PM ✱4·61: ${\sim} (p \supset q) \equiv (p \land {\sim} q)$Proved

  Oct 2026

• PM ✱4·57: ${\sim} ({\sim} p \land {\sim} q) \equiv (p \lor q)$Proved

  Oct 2026

• PM ✱4·65: ${\sim} ({\sim} p \supset q) \equiv ({\sim} p \land {\sim} q)$Proved

  Oct 2026

• PM ✱4·53: ${\sim} (p \land {\sim} q) \equiv ({\sim} p \lor q)$Proved

  Oct 2026

• PM ✱4·32: $((p \land q) \land r) \equiv (p \land (q \land r))$Proved

  Oct 2026

• PM ✱5·7: $((p \lor r) \equiv (q \lor r)) \equiv (r \lor (p \equiv q))$Proved

  Oct 2026

• PM ✱4·56: $({\sim} p \land {\sim} q) \equiv {\sim} (p \lor q)$Proved

  Oct 2026

• PM ✱5·6: $((p \land {\sim} q) \supset r) \equiv (p \supset (q \lor r))$Proved

  Oct 2026

• PM ✱5·21: $({\sim} p \land {\sim} q) \supset (p \equiv q)$Proved

  Oct 2026

• PM ✱5·54: $((p \land q) \equiv p) \lor ((p \land q) \equiv q)$Proved

  Oct 2026

• PM ✱4·76: $((p \supset q) \land (p \supset r)) \equiv (p \supset (q \land r))$Proved

  Oct 2026

• PM ✱5·53: $(((p \lor q) \lor r) \supset s) \equiv (((p \supset s) \land (q \supset s)) \land (r \supset s))$Proved

  Oct 2026

• PM ✱4·52: $(p \land {\sim} q) \equiv {\sim} ({\sim} p \lor q)$Proved

  Oct 2026

• PM ✱4·15: $((p \land q) \supset {\sim} r) \equiv ((q \land r) \supset {\sim} p)$Proved

  Oct 2026

• PM ✱4·42: $p \equiv ((p \land q) \lor (p \land {\sim} q))$Proved

  Oct 2026

• PM ✱4·86: $(p \equiv q) \supset ((p \equiv r) \equiv (q \equiv r))$Proved

  Oct 2026

• PM ✱4·85: $(p \equiv q) \supset ((r \supset p) \equiv (r \supset q))$Proved

  Oct 2026

• PM ✱4·43: $p \equiv ((p \lor q) \land (p \lor {\sim} q))$Proved

  Oct 2026

• PM ✱4·41: $(p \lor (q \land r)) \equiv ((p \lor q) \land (p \lor r))$Proved

  Oct 2026

• PM ✱4·84: $(p \equiv q) \supset ((p \supset r) \equiv (q \supset r))$Proved

  Oct 2026

• PM ✱4·12: $(p \equiv {\sim} q) \equiv (q \equiv {\sim} p)$Proved

  Oct 2026

• PM ✱4·4: $(p \land (q \lor r)) \equiv ((p \land q) \lor (p \land r))$Proved

  Oct 2026

• PM ✱4·37: $(p \equiv q) \supset ((p \lor r) \equiv (q \lor r))$Proved

  Oct 2026

• PM ✱4·36: $(p \equiv q) \supset ((p \land r) \equiv (q \land r))$Proved

  Oct 2026

• PM ✱4·11 (Transp): $(p \equiv q) \equiv ({\sim} p \equiv {\sim} q)$Proved

  Oct 2026

• PM ✱5·55: $((p \lor q) \equiv p) \lor ((p \lor q) \equiv q)$Proved

  Oct 2026

• PM ✱5·501: $p \supset (q \equiv (p \equiv q))$Proved

  Oct 2026

• PM ✱5·42: $(p \supset (q \supset r)) \equiv (p \supset (q \supset (p \land r)))$Proved

  Oct 2026

• PM ✱4·22: $((p \equiv q) \land (q \equiv r)) \supset (p \equiv r)$Proved

  Oct 2026

• PM ✱5·35: $((p \supset q) \land (p \supset r)) \supset (p \supset (q \equiv r))$Proved

  Oct 2026

• PM ✱3·47: $((p \supset r) \land (q \supset s)) \supset ((p \land q) \supset (r \land s))$Proved

  Oct 2026

• PM ✱3·48: $((p \supset r) \land (q \supset s)) \supset ((p \lor q) \supset (r \lor s))$Proved

  Oct 2026

• PM ✱5·31: $(r \land (p \supset q)) \supset (p \supset (q \land r))$Proved

  Oct 2026

• PM ✱5·3: $((p \land q) \supset r) \equiv ((p \land q) \supset (p \land r))$Proved

  Oct 2026

• PM ✱5·36: $(p \land (p \equiv q)) \equiv (q \land (p \equiv q))$Proved

  Oct 2026

• PM ✱4·82: $((p \supset q) \land (p \supset {\sim} q)) \equiv {\sim} p$Proved

  Oct 2026

• PM ✱5·5: $p \supset ((p \supset q) \equiv q)$Proved

  Oct 2026

• PM ✱5·1: $(p \land q) \supset (p \equiv q)$Proved

  Oct 2026

• PM ✱4·83: $((p \supset q) \land ({\sim} p \supset q)) \equiv q$Proved

  Oct 2026

• PM ✱4·45: $p \equiv (p \land (p \lor q))$Proved

  Oct 2026

Posted 50

• PM ✱1 (about the system): completeness of ✱1 for two-valued truth tablesProved

  Oct 2026

• PM ✱5·74: $(p \supset (q \equiv r)) \equiv ((p \supset q) \equiv (p \supset r))$Proved

  Oct 2026

• PM ✱5·75: $((r \supset {\sim} q) \land (p \equiv (q \lor r))) \supset ((p \land {\sim} q) \equiv r)$Proved

  Oct 2026

• PM ✱5·63: $(p \lor q) \equiv (p \lor ({\sim} p \land q))$Proved

  Oct 2026

• PM ✱5·7: $((p \lor r) \equiv (q \lor r)) \equiv (r \lor (p \equiv q))$Proved

  Oct 2026

• PM ✱5·71: $(q \supset {\sim} r) \supset (((p \lor q) \land r) \equiv (p \land r))$Proved

  Oct 2026

• PM ✱5·54: $((p \land q) \equiv p) \lor ((p \land q) \equiv q)$Proved

  Oct 2026

• PM ✱5·42: $(p \supset (q \supset r)) \equiv (p \supset (q \supset (p \land r)))$Proved

  Oct 2026

• PM ✱5·31: $(r \land (p \supset q)) \supset (p \supset (q \land r))$Proved

  Oct 2026

• PM ✱5·33: $(p \land (q \supset r)) \equiv (p \land ((p \land q) \supset r))$Proved

  Oct 2026

• PM ✱5·5: $p \supset ((p \supset q) \equiv q)$Proved

  Oct 2026

• PM ✱5·501: $p \supset (q \equiv (p \equiv q))$Proved

  Oct 2026

• PM ✱5·24: ${\sim} ((p \land q) \lor ({\sim} p \land {\sim} q)) \equiv ((p \land {\sim} q) \lor (q \land {\sim} p))$Proved

  Oct 2026

• PM ✱5·6: $((p \land {\sim} q) \supset r) \equiv (p \supset (q \lor r))$Proved

  Oct 2026

• PM ✱5·16: ${\sim} ((p \equiv q) \land (p \equiv {\sim} q))$Proved

  Oct 2026

• PM ✱5·61: $((p \lor q) \land {\sim} q) \equiv (p \land {\sim} q)$Proved

  Oct 2026

• PM ✱5·32: $(p \supset (q \equiv r)) \equiv ((p \land q) \equiv (p \land r))$Proved

  Oct 2026

• PM ✱5·22: ${\sim} (p \equiv q) \equiv ((p \land {\sim} q) \lor (q \land {\sim} p))$Proved

  Oct 2026

• PM ✱5·41: $((p \supset q) \supset (p \supset r)) \equiv (p \supset (q \supset r))$Proved

  Oct 2026

• PM ✱5·55: $((p \lor q) \equiv p) \lor ((p \lor q) \equiv q)$Proved

  Oct 2026

• PM ✱5·44: $(p \supset q) \supset ((p \supset r) \equiv (p \supset (q \land r)))$Proved

  Oct 2026

• PM ✱5·18: $(p \equiv q) \equiv {\sim} (p \equiv {\sim} q)$Proved

  Oct 2026

• PM ✱5·36: $(p \land (p \equiv q)) \equiv (q \land (p \equiv q))$Proved

  Oct 2026

• PM ✱5·53: $(((p \lor q) \lor r) \supset s) \equiv (((p \supset s) \land (q \supset s)) \land (r \supset s))$Proved

  Oct 2026

• PM ✱5·17: $((p \lor q) \land {\sim} (p \land q)) \equiv (p \equiv {\sim} q)$Proved

  Oct 2026

• PM ✱5·3: $((p \land q) \supset r) \equiv ((p \land q) \supset (p \land r))$Proved

  Oct 2026

• PM ✱5·21: $({\sim} p \land {\sim} q) \supset (p \equiv q)$Proved

  Oct 2026

• PM ✱5·35: $((p \supset q) \land (p \supset r)) \supset (p \supset (q \equiv r))$Proved

  Oct 2026

• PM ✱5·23: $(p \equiv q) \equiv ((p \land q) \lor ({\sim} p \land {\sim} q))$Proved

  Oct 2026

• PM ✱5·19: ${\sim} (p \equiv {\sim} p)$Proved

  Oct 2026

• PM ✱5·15: $(p \equiv q) \lor (p \equiv {\sim} q)$Proved

  Oct 2026

• PM ✱4·65: ${\sim} ({\sim} p \supset q) \equiv ({\sim} p \land {\sim} q)$Proved

  Oct 2026

• PM ✱4·85: $(p \equiv q) \supset ((r \supset p) \equiv (r \supset q))$Proved

  Oct 2026

• PM ✱4·76: $((p \supset q) \land (p \supset r)) \equiv (p \supset (q \land r))$Proved

  Oct 2026

• PM ✱4·73: $q \supset (p \equiv (p \land q))$Proved

  Oct 2026

• PM ✱4·57: ${\sim} ({\sim} p \land {\sim} q) \equiv (p \lor q)$Proved

  Oct 2026

• PM ✱4·83: $((p \supset q) \land ({\sim} p \supset q)) \equiv q$Proved

  Oct 2026

• PM ✱4·61: ${\sim} (p \supset q) \equiv (p \land {\sim} q)$Proved

  Oct 2026

• PM ✱4·86: $(p \equiv q) \supset ((p \equiv r) \equiv (q \equiv r))$Proved

  Oct 2026

• PM ✱4·77: $((q \supset p) \land (r \supset p)) \equiv ((q \lor r) \supset p)$Proved

  Oct 2026

• PM ✱4·7: $(p \supset q) \equiv (p \supset (p \land q))$Proved

  Oct 2026

• PM ✱4·87: ((((p ∧ q) ⊃ r) ≡ (p ⊃ (q ⊃ r))) ∧ ((p ⊃ (q ⊃ r)) ≡ (q ⊃ (p ⊃ r)))) ∧ ((q ⊃ (p ⊃ r)) ≡ ((q ∧ p) ⊃ r))Proved

  Oct 2026

• PM ✱4·56: $({\sim} p \land {\sim} q) \equiv {\sim} (p \lor q)$Proved

  Oct 2026

• PM ✱4·74: ${\sim} p \supset (q \equiv (p \lor q))$Proved

  Oct 2026

• PM ✱4·82: $((p \supset q) \land (p \supset {\sim} q)) \equiv {\sim} p$Proved

  Oct 2026

• PM ✱4·43: $p \equiv ((p \lor q) \land (p \lor {\sim} q))$Proved

  Oct 2026

• PM ✱4·72: $(p \supset q) \equiv (q \equiv (p \lor q))$Proved

  Oct 2026

• PM ✱4·45: $p \equiv (p \land (p \lor q))$Proved

  Oct 2026

• PM ✱4·78: $((p \supset q) \lor (p \supset r)) \equiv (p \supset (q \lor r))$Proved

  Oct 2026

• PM ✱5·1: $(p \land q) \supset (p \equiv q)$Proved

  Oct 2026