**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 \(x\).

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