Consider the following square with the four corners and the center marked as $\text{P, Q, R, S}$ and $\text{T}$ respectively.
Let $\text{X, Y}$ and $\text{Z}$ represent the following operations:
$\text{X:}$ rotation of the square by $180$ degree with respect to the $\text{S – Q}$ axis.
$\text{Y:}$ rotation of the square by $180$ degree with respect to the $\text{P – R}$ axis.
$\text{Z:}$ rotation of the square by $90$ degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point $\text{T}.$
Consider the following three distinct sequences of operation (which are applied in the left to right order).
- $\text{XYZZ}$
- $\text{XY}$
- $\text{ZZZZ}$
Which one of the following statements is correct as per the information provided above?
- The sequence of operations $(1)$ and $(2)$ are equivalent
- The sequence of operations $(1)$ and $(3)$ are equivalent
- The sequence of operations $(2)$ and $(3)$ are equivalent
- The sequence of operations $(1), (2)$ and $(3)$ are equivalent