Discrete Mathematics

---------------------------SYMBOLIC

LOGIC

87

for

x.

This prevents the function from being used on types that may not make sense. For example,

it

might not

make sense to let x

=dog

to the predicate,

P,

because dog is not a number and therefore checking

if

it is a

prime number does not make sense.

In mathematics, we use sets to determine the kinds

of

values a variable can assume. For example, it

might have P(x) but restrict

x by saying x e N (x has to be an element

of

the natural numbers) It is important

to think about how the input is restricted for a predicate. For example, someone tells us

of

a predicate Q(x, y),

we should ask which sets