Question

If $X=\{x:x=8^n-7n-1|n\in N\}$ and $Y=\{y:y=49n-49|n\in N\}$

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

Answer 1

Answer: (A), (C)

$X\cap Y=X$

$X=\{x:x=8^n-7n-1\}=\{0,49,490,....\}$
$Y=\{y:y=49n-49\}=\{0,49,98,147,....\}$
So every elements of X is in Y but every element of Y is not in X.
So $X\subset Y\Rightarrow X\cap Y=X$