JEE Main | 2014Set, Relation and FunctionMedium
Question
If X = {4n - 3n - 1 : n ∈ N} and Y = {9(n - 1) : n ∈ N},
where N is the set of natural numbers, then X ∪ Y is equal to
where N is the set of natural numbers, then X ∪ Y is equal to
Options
A.X
B.Y
C.N
D.Y - X
Solution
X = {(1 + 3)n - 3n - 1, n∈N}
= 32(nC2 + nC3. 3+ ....+3n-2), n ∈ N}
= {Divisible by 9}
Y = {9(n - 1), n ∈ N}
= (All multiples of 9}
So, X ⊆ Y
i.e.,
= 32(nC2 + nC3. 3+ ....+3n-2), n ∈ N}
= {Divisible by 9}
Y = {9(n - 1), n ∈ N}
= (All multiples of 9}
So, X ⊆ Y
i.e.,
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