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Question

If X=8n7n1,nN and Y=49(n1),nN, then -

A
XY
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B
YX
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C
X=Y
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D
None of these
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Solution

The correct option is A XY
Conventional Approach:

For n=1,8n7n1=871=0;
For n=2,8n7n1=64141=49
8n7n1 is a multiple of 49 for all nN.
X contains elements which are multiples of 49 and Y clearly contains all multiples of 49.
XY.

Best Approach:

Put n = 1, X = 0, Y = 0
For n = 2, X = 49, Y = 49
For n = 3, X = 490, Y = 98
X contains elements which are multiples of 49 and Y clearly contains all multiples of 49.
XY.

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