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If X""=""{4^n-3n-1"":""n in N}""a n d""...

If `X""=""{4^n-3n-1"":""n in N}""a n d""Y""=""{9(n-1)"": n in N}` , where N is the set of natural numbers, then `XuuY` is equal to (1) N (2) Y - X (3) X (4) Y

A

N

B

`Y-X`

C

X

D

Y

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `X = {4^(n)-3n-1: n in N}`
`X = {0,9,54,243, …..} " " [put n = 1,2,3, …]`
`Y={9,n-1: n in N} `
` Y= [0,9,18, 27, …} " " ["put " n =1,2,3, …]`
It is clear that, ` X sub Y`
` therefore X cup Y = Y`
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