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Question

If X={4n3n1:nN} and Y={9(n1):nN}, where N is the set of natural numbers, then XY is equal to:

A
N
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B
YX
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C
X
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D
Y
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Solution

The correct option is D Y
X={4n3n1:nN}
=(1+3)n3n1
= nC030+ nC131+ nC232+...+ nCn3n3n1
=9[ nC2+ nC33+ nC432+...+ nCn23n2]
X is multiple of 9
So, X=0,9,54,........(1)
Now, Y={9(n1): nN}
Y is also multiple of 9
So, Y=0,9,18................(2)
From equation (1) and (2)
XY=Y

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