a) What is the difference between the quantification and where P(x, y) is a predicate?

b) Give an example of a predicate P(x, y) such that and have different truth values.

Solution :

Step 1:

a:

We need to define the difference between x and .

We given P(x , y) is a predicate. So it is the multiple quantifiers .

Now

- x is read as “ there exists a number x such that , for every number y in predicate P(x, y).
- is read as “ for every number y , there exists a number x in predicate P(x, y).