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Question

Let X={1,2,3,4,5}. The number of different ordered pairs (Y,Z) that can be formed such that YX,ZX and YZ is empty, is

A
53
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B
52
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C
35
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D
25
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Solution

The correct option is C 35
YZ=ϕY and Z are disjoint subsets of X.
Let aX
Case 1:aY and aZ
Case 2:aZ and aY
Case 3:aY and aZ
So, each element has 3 options.
There are 5 possibilities for a.
Possible number of ordered pairs =35

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