Definition:Conjunction/Semantics of Conjunction

Definition

Let $p \land q$ denote the conjunction of two statements $p$ and $q$.

The conjunction is used to symbolise any statement in natural language such that two substatements are held to be true simultaneously.

Thus it is also used to symbolise the concept of but as well as and.

Thus $p \land q$ can be also interpreted as:

• $p$ and $q$
• $p$ but $q$
• $p$, yet $q$
• $p$, although $q$
• $p$; still, $q$
• $p$; however, $q$
• $p$; on the other hand $q$
• $p$; moreover $q$
• $p$; furthermore, $q$
• $p$; nevertheless, $q$
• Not only $p$ but also $q$
• Despite $p$, $q$

Warning

Beware of the usage of and in natural language which has the following form:

He fell out of bed and broke his leg

which does not mean the same as:

He broke his leg and fell out of bed.

This use of and actually means and then, as it is implicit that the two occurrences are neither simultaneous nor independent, but that the second occurrence happens as a result of the first.

Sources

• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.1$: Simple and Compound Statements
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.1$: Introduction