Question

If $x<n\forall n\in Z,$ then , where $[.]$ denotes the GIF.

• A. $\left[x\right]<n-1$
• B. $\left[x\right]\le n$
• C. $\left[x\right]<n$

Answer 1

The correct option is C $\left[x\right]<n$

Given an integer $n$ such that $\left[x\right]<n$
Now, $\left[x\right]<n\Rightarrow x<n\forall n\in Z$ and vice versa.

Let's take an example.
$x=6.2,n=7$
$x<n\&\left[x\right]=6<7$

Let's take another example:
$x=-2.3,n=-1$
Here, $x<n\&\left[x\right]=-3<n$
Hence, the relation gets satisfied.