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

The correct options are A X ⊂ Y C X ∩ Y = XX ={x:x=8^n 7n 1} ={0, 49, 490,....} Y ={y:y=49n 49} = {0,49, 98,147,....} As nbsp;every elements of X i ...

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Byju's Answer

Standard XII

Mathematics

Subset

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 options are
A $X \subset Y$
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

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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 = {$8^n-7n-1/n \in N$} and Y = {$49(n-1)/n \in N$}, then

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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 options are A X⊂Y 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 options are
A $X \subset Y$
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
$X \subset Y \Rightarrow X \cap Y = X$