Answer to Question #248466 in Real Analysis for Joy

Question

Show that (A -B) U B = A is not necessarily true; that is, find sets A and B for which it is false.

Answer 1

$A-B=\{x:x\epsilon A,x\cancel{\epsilon}B\}$

Let $A=\{1,2,3,4\}$

$B=\{3,4,5,6\}$

$A-B=\{1,2\}$

$(A-B)UB=\{1,2\}U\{3,4,5,6\}$

$=\{1,2,3,4,5,6\}$

$\not =\{1,2,3,4\}=A$

$\therefore (A-B)UB\not =A$

So the given statement is false.