Math 3000   Quiz #4   Spring 2008

If B and C are sets, either prove the following statement or show that it is false (i.e., provide a counterexample).

If x B and B is not a subset of C then x C.

Solution:

The statement is false. A counterexample is given by:

B = {1,2,3}

C = {1,4}

x = 1

Since x B and B is not a subset of C but x C.