Sets

[Kaycee]

Tell whether each of the following is true or false for all sets A, B, or C if False, give a counterexample

(A-B) U A equals (A-B) U (B-A)

 

[stapel]

To show set equality, one usually shows double set inclusion. Pick an element from the left-hand side, and show that it is an element of the right-hand side. Then pick an element of the right-hand side, and show that it is an element of the left-hand side. If the sets are subsets of each other, then they must be equal.

Eliz.

 

[pka]

One can also show that it is not true by counterexample.
[(A\B) U A] ≠ [(A\B) U (B\A)].
If A={1,2,3} & B={2,3,4} then [(A\B) U A]=A.
While [(A\B) U (B\A)]={1,4}.