The statement *P and Q*. is the set of
numbers which satisfies P and Q at the same time. When you write it in set
notation the and corresponds to intersection. It would be written as
{x.:.x.<.5.and.-1..x} which is the same as {x.:.x.<.5}{x.:.-1..x}. Let's use the number line to visualize this.

_______________________________________________Now the statement_{o}_ _ _ _ _ _ _ {x : x < 5} 5 _ _ _ _ _ _ _________________________________________________ -1 {x : -1 x} _ _ _ _ _ _ ____________________________________ _ _ _ _ _ _ -1 {x.:.x.<.5}{x.:.-1..x} 5

________________________________________________ _ _ _ _ _ _ -1 5 ~~~~~~~~~~~~~~~~~~~~~\ /~~~~~~~~~~~~~~~~~~~~~~~~ {x.:.x.<.5}{x.:.-1..x}Here is another example:

Let P be the statement x < 0 and Q be the statement x.>.100. Let's start with P or Q. Using the number line we can see:

_______________{o}_ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ {x : x < 0} 0 _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ __{o}________________ 100 {x : x > 100} _______________{o}_ _ _ _ _ _ _ _ _ _ _ _ _ _ __{o}________________ \ / \ / {x : x < 0 or x > 100}

Now if we were to try and do *P and Q*. the
number line picture would be:

_______________The set of_{o}____________________________{o}________________ 0 100

As you can see *and*. and *or*. are quite different so make sure that
you know the difference between them before continuing.

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