State True or False for the following statements:
$(i)$ $\mathop{C}\limits^{+}H_3$ and $CH_3\mathop{C}\limits^{+}H_2$ both are primary carbocations.
$(ii)$ $(CH_3)_3\mathop{C}\limits^{+}$ is a tertiary carbocation and all carbons are $sp^3$ hybridized.
$(iii)$ $\mathop{C}\limits^{+}H_3$ is trigonal planar.
$(iv)$ $CH_4$ is not trigonal planar.

(N/A) $(i)$ False. $\mathop{C}\limits^{+}H_3$ (methyl carbocation) is not classified as primary,secondary,or tertiary because it is not attached to any alkyl group. $CH_3\mathop{C}\limits^{+}H_2$ is a primary carbocation.
$(ii)$ False. $(CH_3)_3\mathop{C}\limits^{+}$ is a tertiary carbocation,but the positively charged carbon is $sp^2$ hybridized,not $sp^3$.
$(iii)$ True. The methyl carbocation $\mathop{C}\limits^{+}H_3$ has three bonding pairs and no lone pairs on the central carbon,resulting in $sp^2$ hybridization and a trigonal planar geometry.
$(iv)$ True. $CH_4$ (methane) has four bonding pairs and no lone pairs,resulting in $sp^3$ hybridization and a tetrahedral geometry,not trigonal planar.