Philosophy Index

Conjunction

Conjunction is a truth-functional operator in logic which is equivalent to the word “and”.

If P is known and Q is known, we may say P and Q, or formally:

P ∧ Q

This may be read as “P and Q” or “it is the case that both P and Q”.

In symbolic logic, the conjunction symbol ( ∧ ) is used to symbolize a conjunction. The ampersand ( & ) or the word AND, and in some cases, a dot ( · ), are used in some logical systems. For consistency, this site will always use the ∧ symbol.

Truth values

The following table illustrates the possible truth values of P ∧ Q, given each possible valuation of its terms, P and Q. Note that P ∧ Q is true if, and only if, P is true, and Q is true.

P Q P ∧ Q
T T T
T F F
F T F
F F F

English conjunctions

The conjunction is normally associated with the English word “and”. However, many other words function as conjunctions in English. For instance, the following words and phrases may also take the form of a conjunction:

  • but
  • so
  • as well as
  • though
  • whereas

Some of these phrases may seem to lose some information when translated into symbolic logic. For instance, the phrase “John isn't a lawyer, but he is a paralegal” may be symbolized as ¬L & P, if L means “John is a lawyer” and P means “John is a paralegal”. The choice of the English word “but” is meant to show contrast between the two propositions, rather than simply say that both are the case.