Question

If $X=\{8^n-7n-1|n\in N\}$ and

$Y=\{49n-49|n\in N\}.$

Then

• A. $X=Y$
• B. $Y\subset X$
• C. $X\subset Y$
• D. $X\cap Y=\varphi$

Answer 1

The correct option is C $X\subset Y$

Given : $X=\{8^n-7n-1|n\in N\}$ and

$Y=\{49n-49|n\in N\}$

$X=\{0,49,490,...\}$

$Y=\{0,49,98,147,...,490,...\}$

Clearly, every element of X is in Y but every element of Y is not in X.

$\therefore X\subset Y$

Hence, option (A) is correct.