Both inputs must be TRUE for output to be TRUE. The strictest gate: no partial credit, no exceptions.
| A | B | A AND B |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
At least one input TRUE yields TRUE. The inclusive gate: generous, accommodating.
Inverts everything. TRUE becomes FALSE, FALSE becomes TRUE. The contrarian.
| A | B | A XOR B |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | F |
The classical deductive machine. Two premises enter. One conclusion exits. If the form is valid and premises are true, the conclusion is inescapable.
"THIS STATEMENT IS FALSE"
If true, then it's false. If false, then it's true. The logic engine encounters its first infinite loop. Status: UNRESOLVABLE.
"THE SET OF ALL SETS THAT DO NOT CONTAIN THEMSELVES"
Does it contain itself? If yes, then no. If no, then yes. Set theory hits a wall. Mathematics reboots.