Let $$X$$ = {1, 2, 3, 4, 5}. The number of different ordered pairs $$(Y, Z)$$ that can formed such that $$Y \subseteq X,Z \subseteq X$$ and $$Y \cap Z$$ empty is :
A.
$${5^2}$$
B.
$${3^5}$$
C.
$${2^5}$$
D.
$${5^3}$$
Answer :
$${3^5}$$
Solution :
Let $$X$$ = {1, 2, 3, 4, 5}
Total no. of elements = 5
Each element has 3 options. Either set $$Y$$ or set $$Z$$ or none. $$\left( {\because Y \cap Z = \phi } \right)$$
So, number of ordered pairs $$ = {3^5}$$
Releted MCQ Question on Calculus >> Sets and Relations
Releted Question 1
If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$ equals.