### Logical Connectives:Conjunction

A conjunction is a way of asserting two component propositions, called conjuncts, in a single statement.

Example:

The rent is due, and I have no money.

For this to be true, both conjuncts must be true. And if the conjuncts are both true, the conjunction is true.

The conjunction sign (called the "dot") represents this relationship between the truth of the components and the truth of the compound statement as a whole.

It is useful to formulate this relationship graphically. The form of a conjunction is pq. The propositions p and q can be any component statements, and each of them can be either true or false (represented by T and F, as on a true-false test). So we have four possibilities to consider, and we lay them out in a truth table:
 p q pq T T T Conjunction F T F T F F F F F
The table shows that pq is true only in the first case, where each of the component statements, p and q, have the truth value T. In all other cases, pq is false. This connective may be indicated by other words in English besides "and." Consider the following:

I want to go skydiving, but I have a sprained ankle.

Although steel rusts, it is often used in underwater construction.

Julie worked hard to pass the course; nevertheless, she failed.

In each case, the underlined word suggests some incongruity between the component propositions, but the sentence still asserts both components; the sentence is true if and only if the components are both true. Each of these sentences, therefore, has the logical form of a conjunction.

Conjunction | Negation | Disjunction | Conditional
Logical Connectives