Conjunction Glossary
Definition
The conjunction connective 'AND' results in a formula A AND B which is true if and only if A is true and B is true. A and B are said to be its conjuncts.
Connectives with similar truth conditions in natural languages are also taken to express conjunction. The word 'and' in English, taken in a truth-functional sense, is the intended analogue of the formal connective.
Comments
'And' is the neutral connective: its function is to combine sentences into a single sentence without changing the content of what is asserted. For instance, 'Africa is hot and Greenland is cold' says the same thing as 'Africa is hot; Greenland is cold.'
The truth table is:
| AND | 0 | 1 |
| 0 | 0 | 0 |
| 1 | 0 | 1 |
The natural deduction rules for conjunction express the fact that a conjunction says the same thing as its conjuncts: A AND B is an immediate consequence of A and B, and conversely each of the conjuncts is an immediate consequence of the conjunction.
Examples
- 'Snoopy is a pet and a carnivore' expresses the facts that he is a pet and that he is a carnivore. It is true because he eats meat, which is what carnivores do, and he is Charlie Brown's dog and therefore a pet.
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The following proof illustrates the rules for
conjunction:
SP {p AND q, p AND r ⊢ q AND r} PL {1} {1} {p AND q} {A} PL {2} {2} {p AND r} {A} PL {1} {3} {q} {1 ANDE} PL {2} {4} {r} {2 ANDE} PL {1,2} {5} {q AND r} {3, 4 ANDI} EP