Think clearly.
Both conditions must be true. The conjunction operator returns true only when every input is true. It is the strictest gate -- no exceptions, no compromises.
At least one condition must be true. The disjunction operator is generous -- it yields true if any input shines. One truth is enough.
Inversion. The negation operator flips truth to falsehood and falsehood to truth. It is the simplest and most powerful transformation in logic.
If the premise holds, the conclusion follows. The conditional is the backbone of deductive reasoning -- it only fails when truth leads to falsehood.
| P | Q | P & Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
| P | Q | P || Q |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
| P | ¬P |
|---|---|
| T | F |
| F | T |
| P | Q | P ⇒ Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Premise 1
All humans are mortal.
Premise 2
Socrates is a human.
Conclusion
Therefore, Socrates is mortal.