# Parenthesis/Natural Language/Examples

## Examples of Use of Parenthesis in Natural Language

### Use of Either

Consider the sentence:

More stringent anti-pollution measures will be enacted and the laws will be strictly enforced or the quality of life will be degraded still further.

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

$p$ is the simple statement More stringent anti-pollution measures will be enacted
$q$ is the simple statement The laws will be strictly enforced
$r$ is the simple statement The quality of life will be degraded still further.

As it stands, it is not clear how the grouping is to be done.

The word either is often used together with the instance of or to tell the reader what the scope of the disjunction actually is.

Hence:

Either more stringent anti-pollution measures will be enacted and the laws will be strictly enforced, or the quality of life will be degraded still further

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

while:

More stringent anti-pollution measures will be enacted, and either the laws will be strictly enforced or the quality of life will be degraded still further

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

### Use of Both

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 $\lnot \paren {p \land q}$.