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Question

If X  = {8n – 7n – 1 : nN} and Y = {49n – 49 : nN}. Then,
(a) XY
(b) YX
(c) X = Y
(d) XY = ϕ


Solution

X=8n-7n-1, nNY=49n-49; nNSince 8n-7n-1=1+7n-7n-1                              =1+7n+nC272+nC373+....+7n-7n-1                              =1+7n+nC249+nC373+ .... +7n-7n-1                              =72nC2+nC37+ .... +7n-2                              =49nC2+nC37+ ...+7n-2i.e. 8n-7n-1 is a multiple of 49i.e. XYHere X=0, 49, 490, 4067, ....         Y=0, 49, 98, .....YX since 98 x XY

Hence, the correct answer is option A.

Mathematics
RD Sharma XI (2020, 2021)_Volume 1
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