Mathematics Homework Solutions
Problem
#253858

Discrete Structures

In basic algebra the following Theorem is used frequently.  
If x,y and z are any three real numbers and if x + z = y + z  then x = y.  

The analogous statement for sets would read:  Let A, B, and C be any three sets.

If  A   B = A   C then B = C.

Prove in detail that this statement is false.  (Hint:  Give a counterexample)

Then,

Write the converse of the above statement and show through an example that it is true.


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