Select the correct option using $T$ (True) or $F$ (False) for the following statements regarding crystal systems:
$(1)$ Crystal system: Cubic,Axial distance: $a = b = c$,Axial angle: $\alpha = \beta = \gamma = 90^{\circ}$,Example: $Cu, KCl$
$(2)$ Crystal system: Monoclinic,Axial distance: $a \neq b \neq c$,Axial angle: $\alpha = \gamma = 90^{\circ}, \beta \neq 90^{\circ}$,Example: $PbCrO_4$
$(3)$ Crystal system: Trigonal (Rhombohedral),Axial distance: $a = b = c$,Axial angle: $\alpha = \beta = \gamma \neq 90^{\circ}$,Example: $CaCO_3, HgS$
$(4)$ Crystal system: Triclinic,Axial distance: $a \neq b \neq c$,Axial angle: $\alpha \neq \beta \neq \gamma \neq 90^{\circ}$,Example: $K_2Cr_2O_7, CuSO_4 \cdot 5H_2O$