Parenthesis/Natural Language/Examples/Use of Both

Examples of Use of Parenthesis in Natural Language

Consider the sentence:

Alice and Betty will not be elected.

This is of the form $\lnot p \land q$, where:

$p$ is the simple statement Alice will be elected

$q$ is the simple statement Betty will be elected.

The word both together with the word not can be used to clarify.

Hence:

Alice and Betty will both not be elected

corresponds with the form $\paren {\lnot p} \land \paren {\lnot q}$

while:

Alice and Betty will not both be elected

corresponds with the form $\lnot \paren {p \land q}$.

Sources

• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.1$: Simple and Compound Statements