The prompt for this questions is whether `10^n is in O(2^n)`

is True or False. The quiz shows the correct answer to be false, but what if c * 2 is greater than 10, as an example lets say c = 6 and n0 = 1. In that case 10^1 less than or equal to 6 * 2^1 evaluates to true so I am confused.

Considering the proof by contradiction approach:

10^n is in O(2^n)

Hence, 10^n <= c * (2^n)

Assuming c = 2 and n = 2,

10^2 <= 2*2^2
100 <= 8 -> this is not true
Therefore, it is not valid for every case. So, 10^n is not in O*(2^n).