Test Index

AIEEE 2012 Solved Paper

Section: Mathematics

© examsnet.com

Question : 89 of 89

Marks: +1, -0

Let

X=\{1,2,3,4,5\}

. The number of different ordered pairs

(Y, Z)

that can be formed such that

Y \subseteq X, Z \subseteq X

Y \cap Z

$3^{5}$
$2^{5}$
$5^{3}$
$5^{2}$

Solution:

For any element

x_i

present in

X, 4

cases arises while making subsets

Y

and

Z

.

Case-

1: x_i \in Y, x_i \in Z \Rightarrow Y \cap Z \neq \phi

Case-

2: x_i \in Y, x_i \notin Z \Rightarrow Y \cap Z = \phi

Case-

3: x_i \notin Y, x_i \in Z \Rightarrow Y \cap Z = \phi

Case-

4: x_i \notin Y, x_i \notin Z \Rightarrow Y \cap Z = \phi

\therefore

For every element, number of ways

=3

for which

Y \cap Z = \phi

\Rightarrow

Total ways

=3 \times 3 \times 3 \times 3 \times 3[ \because

no. of elements in set

X=5]

=3^{5}

© examsnet.com

Go to Question:

Prev Question