If X-4n-3 n-1- n - N and Y-9n-1- n - N - where N is the set of natural numbers- then X - Y is equal to-A- NB- XC- Y - XD- Y

The correct option is D Y4^n 3n 1 = (1+3)^n 3n 1 =[^nC_0 + ^nC_1 .3+^nC_2. 3^2 + ⋯ +^nC_n 3^n] 3n 1 =9[^nC_2 + ^nC_3.3 + ⋯ +^nC_n.3^n 2] ∴ 4^n 3n 1 is a ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Subset

If X=4n-3 n-1...

Question

If $X = {4^{n} - 3 n - 1 : n ϵ N} a n d Y = {9 (n - 1) : n ϵ N}$ , where N is the set of natural numbers, then $X \cup Y$ is equal to:

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Y - X

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B Y
$4^{n} - 3 n - 1 = (1 + 3)^{n} - 3 n - 1 = [^{n} C_{0} +^{n} C_{1} .3 +^{n} C_{2} . 3^{2} + \dots +^{n} C_{n} 3^{n}] - 3 n - 1 = 9 [^{n} C_{2} +^{n} C_{3} .3 + \dots +^{n} C_{n} {.3}^{n - 2}]$
$∴ 4^{n} - 3 n - 1$ is a multiple of 9 for all n.
$∴$ X = {x : x is a multiple of 9}
Also, $Y = 9 (n - 1) : n ϵ N =$ {All multiples of 9}
Clearly $X \subseteq Y . ∴ X \cup Y = Y$

Suggest Corrections

Similar questions

Q. If

X = {4^{n} - 3 n - 1 : n \in N}

and

Y = {9 (n - 1) : n \in N}

, where

N

is the set of natural numbers, then

X \cup Y

is equal to:

Q. If

X = {4^{n} - 3 n - 1 : n ϵ N} a n d Y = {9 (n - 1) : n ϵ N}

, where N is the set of natural numbers, then

X \cup Y

is equal to:

Q. If

X = {4^{n} - 3 n - 1 : n \in N}

and

Y = {9 (n - 1) : n \in N}

where

N

is the set of natural numbers, then

X \cup Y

is equal to

Q. If

X = {4^{n} - 3 n - 1 : n \in N}

and

Y = {9 (n - 1) : n \in N}

, where N is the set of natural numbers, then

X \cup Y

is equal to:

If X = { $4^{n}$ - 3n - 1 : n ∈ N} and Y = { 9(n-1) : n ∈ N}, then X ∪ Y is equal to

Join BYJU'S Learning Program

If X={4n−3n−1 : nϵN} and Y={9(n−1):nϵN}, where N is the set of natural numbers, then X∪Y is equal to:

The correct option is B Y4n−3n−1=(1+3)n−3n−1=[nC0+nC1.3+nC2.32+⋯+nCn3n]−3n−1=9[nC2+nC3.3+⋯+nCn.3n−2] ∴ 4n−3n−1 is a multiple of 9 for all n. ∴ X = {x : x is a multiple of 9} Also, Y=9(n−1):nϵN= {All multiples of 9} Clearly X⊆Y. ∴ X∪Y=Y

If $X = {4^{n} - 3 n - 1 : n ϵ N} a n d Y = {9 (n - 1) : n ϵ N}$ , where N is the set of natural numbers, then $X \cup Y$ is equal to: