Statement I: In the tert-butyl carbocation (CH3)3C+, there are three methyl groups attached to the carbocationic carbon. Each methyl group has 3 α-hydrogens, making a total of 9 α-hydrogens. Thus, 9 hyperconjugation interactions are possible, which significantly stabilize the carbocation. Statement I is true.
Statement II: In the methyl carbocation CH3+, there are no α-carbons and consequently no α-hydrogens. Hyperconjugation requires the presence of at least one α-hydrogen on a carbon adjacent to the sp2 hybridized carbocation center. Therefore, zero hyperconjugation interactions are possible in CH3+. Statement II is false because it claims three hyperconjugation interactions are possible.
Conclusion: Statement I is true but Statement II is false.