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) $A\cap \overline{B}$
(c) $\overline{A}\cap \overline{B}$
(d) $\overline{A\cap B}$

Answer 1

(b) $A\cap \overline{B}$

A = {x:x is a multiple of 3}
A = $\left\{\mathrm{3,}\mathrm{6,}\mathrm{9,}\mathrm{12,}\mathrm{15,}\mathrm{18,}\mathrm{21,}\mathrm{24,}\mathrm{27,}\mathrm{30,}\mathrm{33,}\mathrm{36,}\mathrm{39,}\mathrm{42,}\mathrm{45,}\mathrm{48,}...\right\}$

B = {x:x is a multiple of 5.}
B = $\left\{5,10,15,20,25,30,35,40,45,50,...\right\}$

Now, we have:
A$-$B = $\left\{3,6,9,12,18,21,24,27,33,36,39,42,48,...\right\}$
= $A\cap \overline{B}$