Do you know its property ?-12

Statement-1 : $e^{\pi}>\pi^e$

Statement-2 : The curves $y^2=4ax$ and $x^2=4by$ intersect at $90^{\circ}$ at some point.

Statement-3 : $f(x)= \begin{cases} x+1, \quad -1 \leq x <0 \\ 0, \quad \quad \quad \quad x=0 \\ x-1, \quad \quad 0 <x \leq 1 \end{cases}$ .

The absolute maximum value of $f(x)$ is $1$ on the closed interval $[ -1,1]$

Statement-4 : The curves $xy=4$ and $x^2+y^2=8$ never touch each other.

Which of the above statements are false ?

You can try more such problems of the set Do you know its property ?