If A = {x : x is a multiple of 3} and ,
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:

$A-B=\{3,6,9,12,18,21,24,27,33,36,39,42,48, \ldots\}$

$=A \cap \bar{B}$

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