- (B ⊃ C) ⊃ (A ⊃ B)
| A | B | C | (B | ⊃ | C) | ⊃ | (A | ⊃ | B) |
| B | B | B | (B | B | B) | B | (B | B | B) |
| B | B | S | (B | S | S) | B | (B | B | B) |
| B | S | B | (S | B | B) | S | (B | S | S) |
| B | S | S | (S | B | S) | S | (B | S | S) |
| S | B | B | (B | B | B) | B | (S | B | B) |
| S | B | S | (B | S | S) | B | (S | B | B) |
| S | S | B | (S | B | B) | B | (S | B | S) |
| S | S | S | (S | B | S) | B | (S | B | S) |
- [(A ^ B) ^ C] v [(A ^ C) v (A ^ B)]
| A | B | C | [(A | ^ | B) | ^ | C] | v | [(A | ^ | C) | v | (A | ^ | B)] |
| B | B | B | [(B | B | B) | B | B] | B | [(B | B | B) | B | (B | B | B) |
| B | B | S | [(B | B | B) | S | S] | B | [(B | S | S) | B | (B | B | B) |
| B | S | B | [(B | S | S) | S | B] | B | [(B | B | B) | B | (B | S | S) |
| B | S | S | [(B | S | S) | S | S] | S | [(B | S | S) | S | (B | S | S) |
| S | B | B | [(S | S | B) | S | B] | S | [(S | S | B) | S | (S | S | B) |
| S | B | S | [(S | S | B) | S | S] | S | [(S | S | S) | S | (S | S | B) |
| S | S | B | [(S | S | S) | S | B] | S | [(S | S | B) | S | (S | S | S) |
| S | S | S | [(S | S | S) | S | S] | S | [(S | S | S) | S | (S | S | S) |
- A ≡ (B v C)
| A | B | C | A | ≡ | (B | v | C) |
| B | B | B | B | B | (B | B | B) |
| B | B | S | B | B | (B | B | S) |
| B | S | B | B | B | (S | B | B) |
| B | S | S | B | S | (S | S | S) |
| S | B | B | S | S | (B | B | B) |
| S | B | S | S | S | (B | B | S) |
| S | S | B | S | S | (S | B | B) |
| S | S | S | S | B | (S | S | S) |