Discrete Mathematics

90 DISCRETE

MATHEMATIC..._---------------------------

The notion

of

x

2

and

~

are not allowed in formal defmition and so the above would not be a legal

Boolean formula.

To

make it legal, we would have to write something like:

Vx

P(x),

where

we

think

of

P(x) as meaning x

2

~

x (which is a predicate since it returns true

or

false, once x has been

chosen). However, it is easier to read

'llxED

x

2

~x

rather than figure out what P means in

Vx

P(x).

1.28

UNDERSTANDING QUANTIFIERS

What does

Vx

P(x)

mean? We can read 'II as "for all'', so the entire statement can be read as "for all x,

P

of

x".

If

we add a domain, things can be made clearer. So,