Question:
If A = {x : x is a multiple of 3} and , B = {x : x is a multiple of 5}, then A − B is
(a) $A \cap B$
(b) $A \cap \bar{B}$
(c) $\bar{A} \cap \bar{B}$
(d) $\overline{A \cap B}$
Solution:
(b) $A \cap \bar{B}$
A = {x:x is a multiple of 3}
$A=\{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48, \ldots\}$
B = {x:x is a multiple of 5.}
$B=\{5,10,15,20,25,30,35,40,45,50, \ldots\}$
Now, we have:
$A-B=\{3,6,9,12,18,21,24,27,33,36,39,42,48, \ldots\}$
$=A \cap \bar{B}$