**
Statement 1
**

$\left[ x+\frac { 1 }{ 2 } \right]$
is an
*
odd
*
function, while
$\cos { \pi x }$
is an
*
even
*
function.

**
Statement 2
**

$\left[ x+\frac { 1 }{ 2 } \right] \cos { \pi x }$
is an
*
odd
*
function.

**
Statement 3
**

Product of an
*
odd
*
function and an
*
even
*
function is an
*
odd
*
function.

$[x ]$ is the greatest integer less than or equal to $x$ .

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

Statement one is incorrect since $f(\frac{1}{2}) = 1$ , but $f(-\frac{1}{2}) = 0$ .

(Where $f = [x+\frac{1}{2}]$ )

However, since the only place where that inconsistency exists is at $\dfrac{n}{2}$ for odd $n$ , and $cos(\pi x)$ is zero at those values, the second statement is true.

Bye the way, it looks like its now time to post a "200 follower" problem! :0) Congrats!