If X- x-x-8n - 7n -1- n - and Y -y-y-49n-49- n - then which of the following is are TRUE-

X ={x:x=8^n 7n 1} ={0, 49, 490,....} Y ={y:y=49n 49} = {0,49, 98,147,....} As nbsp;every elements of X is in Y but every element of Y is not in X, ...

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Byju's Answer

Standard XIII

Mathematics

Intersection of Sets

If X= x:x=8n ...

Question

If $X = {x : x = 8^{n} - 7 n - 1, n \in N}$ and $Y = {y : y = 49 n - 49, n \in N},$ then which of the following is (are) TRUE?

X \subset Y

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Y \subset X

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X \cap Y = X

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X \cap Y = Y

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Solution

The correct option is C $X \cap Y = X$
$X = {x : x = 8^{n} - 7 n - 1} = {0, 49, 490, . . . .} Y = {y : y = 49 n - 49} = {0, 49, 98, 147, . . . .}$

As every elements of $X$ is in $Y$ but every element of $Y$ is not in $X$ , so
$X \subset Y \Rightarrow X \cap Y = X$

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Similar questions

Q. If

X = {x : x = 8^{n} - 7 n - 1 | n \in N}

and

Y = {y : y = 49 n - 49 | n \in N}

Q. If

X = {x : x = 8^{n} - 7 n - 1, n \in N}

and

Y = {y : y = 49 n - 49, n \in N},

then which of the following is (are) TRUE?

If $X = {8^{n} - 7 n - 1 | n ϵ N}$ and $Y = {49 n - 49 | n ϵ N}$ , then

Q. If

X = {8^{n} - 7 n - 1}

and

Y = {49 n - 49}

, where

n \in N

, then find the relation between

X

and

Y .

Q. If X = {8ⁿ – 7n – 1 : n ∈ N} and Y = {49n – 49 : n ∈ N}. Then,
(a) X ⊂ Y
(b) Y ⊂ X
(c) X = Y
(d) X ∩ Y = ϕ

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If X={x:x=8n−7n−1,n∈N} and Y={y:y=49n−49,n∈N}, then which of the following is (are) TRUE?

The correct option is C X∩Y=XX={x:x=8n−7n−1} ={0,49,490,....}Y={y:y=49n−49} ={0,49,98,147,....} As every elements of X is in Y but every element of Y is not in X, so X⊂Y⇒X∩Y=X

If $X = {x : x = 8^{n} - 7 n - 1, n \in N}$ and $Y = {y : y = 49 n - 49, n \in N},$ then which of the following is (are) TRUE?

The correct option is C $X \cap Y = X$
$X = {x : x = 8^{n} - 7 n - 1} = {0, 49, 490, . . . .} Y = {y : y = 49 n - 49} = {0, 49, 98, 147, . . . .}$

As every elements of $X$ is in $Y$ but every element of $Y$ is not in $X$ , so
$X \subset Y \Rightarrow X \cap Y = X$