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Subset and Superset

If X =8n − 7n...

Question

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

A

X \subset Y

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B

Y \subset X

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C

X = Y

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D

X \subset̸ Y

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Solution

The correct option is A $X \subset Y$
Putting $n = 1, 2, 3, . . .$ in the sets
$X = {8^{n} - 7 n - 1 | n \in N} = {0, 49, 490, . . .}$
$Y = {49 (n - 1) | n \in N} = {0, 49, 98, . . .}$
From here, clearly $X \subset Y$

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

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

then which of the following is (are) TRUE?

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

X = 8^{n} - 7 n - 1, n \in N a n d Y = 49 (n - 1), n \in N

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If X = { $8^{n} - 7 n - 1 : n ϵ N$ } and Y = { $49 (n - 1) : n ϵ N$ }, then prove that $X \subseteq Y$ .

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Subset and Superset

Standard XII Mathematics

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