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  • Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs  that can be formed such that  <img al

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\; and\; Y\cap Z  is empty, is

Option: 1

5^{2}


Option: 2

3^{5}


Option: 3

2^{5}


Option: 4

5^{3}


Answers (1)

best_answer

X=\left \{ 1,2,3,4,5 \right \};Y \subseteq X,Z\subseteq X,Y \cap Z=\phi

Let us consider an element "a" from set X

CASE 1: a \in Y and a \in Z

CASE 2: a \in Y and a \notin Z

CASE 3: a \notin Y and a \in Z

CASE 4: a \notin Y and a \notin Z

Only Case 1 has common sets in Y and Z

So

a has total 3 cases

Hence Total Number of Ways=3x3x3x3x3

\text{Number \; of \; ways }=3^{5}

Posted by

Ajit Kumar Dubey

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