# Please explain this questionLet X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y⊆X, Z⊆X and Y∩Z is empty, is

let an element $a\in X$
therefore following are the cases:

since the given condition is $Y\cap Z=\varphi$
therefore for any element of X , there are 3 ways.
either it is an element of Y or it is an element of Z or it is neither the element of Y nor Z
thus the number of ordered pairs = 3*3*3*3*3 = ${3}^{5}$

hope this helps you

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