Aspire Faculty ID #18385 · Topic: AMU MCA 2016 · Just now
AMU MCA 2016

If $X = {4^n - 3n - 1 \mid n \in N}$ and $Y = {9(n-1) \mid n \in N}$, then

Solution

Check divisibility: $4^n - 3n - 1 \equiv 1 - 3n - 1 \equiv -3n \equiv 0 \ (\text{mod } 3)$ Also divisible by $3$ again ⇒ multiple of $9$ So $X \subset Y$ Final Answer: $\boxed{X \subset Y}$
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