Question

If A={1,3,5,7,9,11,13,15,17) and B={2,4,
-18) and N is the Universal Set then A compliment union[{A union B} intersection B compliment) is
a)A
b)N
С)В
d)None of these​

Answer 1

GIVEN :

If $A={\{1,3,5,7,9,11,13,15,17}\}$  and $B={\{2,4,6,8,10,12,14,16,18}\}$ and N is the Universal Set

TO FIND :

The set $A^{\prime}\bigcup ((A\bigcup B)\bigcap B^{\prime})$ is equal to:

SOLUTION :

Given that the sets $A={\{1,3,5,7,9,11,13,15,17}\}$ and $B={\{2,4,6,8,10,12,14,16,18}\}$ and N is the Universal Set

That is $U={\{1,2,3,4,5,6,7,...}\}=N$

Now find $A\bigcup B$ we have that,

$A\bigcup B={\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}\}$

$A^{\prime}={\{2,4,6,8,10,12,14,16,...}\}$

$B^{\prime}={\{1,3,5,7,9,11,13,15,17,...}\}$

$(A\bigcup B)\bigcap B^{\prime}={\{1,3,5,7,9,11,13,15,17}\}$

$A^{\prime}\bigcup((A\bigcup B)\bigcap B^{\prime})={\{2,4,6,8,10,12,14,16,...}\}\bigcup {\{1,3,5,7,9,11,13,15,17}\}$

$={\{1,2,3,4,5,6,7,8,9,10,....}\}=N$

∴ $A^{\prime}\bigcup((A\bigcup B)\bigcap B^{\prime})={\{1,2,3,4,5,6,7,8,9,10,....}\}=N$ where N is the universal set and is equal to the set of all natural numbers.

∴ option B) N is correct.

∴ $A^{\prime}\bigcup((A\bigcup B)\bigcap B^{\prime})=N$