If X = 4 n - 3 n - 1 : n ∈ N and Y = 9 n - 1 : n ∈ N , then X ∩ Y =

Question

If X = 4 n - 3 n - 1 : n ∈ N and Y = 9 n - 1 : n ∈ N , then X ∩ Y =, X, Y, ϕ, 0

MARKS App · Accepted Answer

X = { 4 n − 3 n − 1 : n ∈ N } X = { ( 1 + 3 ) n − 3 n − 1 : n ∈ N } X = { 1 + 3 n + 3 2 n ( n − 1 ) 2 ! + 3 3 n ( n − 1 ) ( 2 n − 1 ) 6 ....3 n − 1 } X = { 3 2 ( n − 1 ) n ( 1 2 ! + 3 ( 2 n − 1 ) 6 + ..... ) } X = { 9 ( n − 1 ) n ( 1 2 ! + ...... ) } Y = { 9 ( n − 1 ) : n ∈ N } ∴ X ⊆ Y ∴ X ∩ Y = X (or) Put n = 1 , 2 , 3 , 4 , 5 , 6 , ..... in X and Y X = { 0 , 9 , 54 , .... } Y = { 0 , 9 , 18 , 27 , 36 , 45 , 54 , 63...... } X ⊆ Y ∴ X ∩ Y = X

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