Determine if the set is closed for the given operation. 
a. the set of integers for multiplication.
-----------------------------
Ask the question:  Can you multiply your way out of the set of integers?

Let's see:  Multiply integer 2 time integer 3.  You get 6 which is also
an integer.  So you didn't multiply your way out of the set of integers.
How about a negative integer like -7, multiply that by 8.  You get -56
which is also an integer.  So you didn't multiply your way out of the set
of integers.  So it looks as though you cannot multiply your way out of
the set of integers, because if you multiply two integers you always get
another integer.  So the answer is: the set of integers is CLOSED for
multiplication.  
------------------------------
b. the set of positive integers for subtraction.
------------------------------
Ask the question:  Can you subtract your way out of the set of positive
integers?

Let's see:  Subtract positive integer 3 from positive integer 2.  You get -1,
which is NOT a positive integer.  So you subtracted your way out of the set of
positive integers into the set of negative integers.  So the answer is:
the set of positive integers is NOT CLOSED for subtraction.  

------------------------------
c. the set of negative integers for addition.
------------------------------

Ask the question:  Can you add your way out of the set of negative integers?

Let's see:  Add negative integer -2 and negative integer -3.  You get -5 which
is also a negative integer.  So you didn't add your way out of the set of
negative integers.  In fact you can't add your way out of negative integers, so
the answer is: the set of negative integers is CLOSED for addition.

---------------

Edwin