$\{$:$Q_1)$

$($a$)($i$)$ Explain what a predicate is$.$ Give two original examples to illustrate the

definition.

$($ii$)$ Consider the following statement:

We shall go to the park tomorrow if it rains today.

Introduce notation for any relevant sub$-$statements and then clearly identify

the logical structure of the statement.

$($b$)$ Let $P$ denote the set of primes. The following is a famous conjecture $($a state$-$

ment that has not been proved or disproved, but that many suspect to be true$)$

concerning $P$ :