Floor function

Algebra Level 3

If $x$ and $y$ are the real numbers with $x, y \geq 1$ then which of the following is always true?

Bonus: You may guess it but can you prove it?

Note :This question is a part of set KVPY 2014 SB

\lfloor 2^{x} \rfloor \leq 2^{\lfloor x \rfloor}

\lfloor x+y \rfloor \leq \lfloor x \rfloor + \lfloor y \rfloor

\frac{\lfloor x \rfloor}{\lfloor y \rfloor}\ge \left \lfloor \frac{x}{y} \right \rfloor

\lfloor xy \rfloor \leq \lfloor x \rfloor \lfloor y \rfloor

0 solutions

No explanations have been posted yet. Check back later!