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 <= 22^2
100 <= 8 -> this is not true
Therefore, it is not valid for every case. So, 10^n is not in O(2^n).