Assignment:
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 U B = A U 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.
Provide complete and step by step solution for the question and show calculations and use formulas.