This is how AND works in Mathematica

And[1 > 0, 1 > 1]

This is how OR works in Mathematica

Or[1 > 0, 1 > 1]

Testing several propositions.

Table[(x^2) > x, {x, -5, 5, 1}]

Now testing connecting all the above propositions with AND.

Apply[And, Table[(x^2) > x, {x, -5, 5, 1}]]

Now testing connecting all the above propositions with OR.

Apply[Or, Table[(x^2) > x, {x, -5, 5, 1}]]

Now testing the negations of the individual propositions connected again with OR.

Apply[Or, Table[Not[(x^2) > x], {x, -5, 5, 1}]]

Today is an interesting date 20110111, but it is not a prime date.

PrimeQ[20110111]

FactorInteger[20110111]