Given below are two statements:

Statement I: $2,6$-diethylcyclohexanone and $6$-methyl-$2$-n-propylcyclohexanone are metamers.

Statement II: $2,2,6,6$-tetramethylcyclohexanone exhibits keto-enol tautomerism.

In the light of the above statements, choose the correct answer from the options given below

Statement I: Metamerism arises due to different alkyl chains on either side of a polyvalent functional group. In ketones, the carbonyl group ($>C=O$) acts as the polyvalent functional group. In $2,6$-diethylcyclohexanone, the alkyl groups attached to the $\alpha$-carbons are two ethyl groups. In $6$-methyl-$2$-n-propylcyclohexanone, the alkyl groups are a methyl group and an n-propyl group. Since the alkyl groups around the carbonyl group are different while the molecular formula remains the same, they are metamers. Thus, Statement I is true.

Statement II: For a ketone to exhibit keto-enol tautomerism, it must have at least one $\alpha$-hydrogen atom. In $2,2,6,6$-tetramethylcyclohexanone, the $\alpha$-carbons (C$2$ and C$6$) are bonded to two methyl groups each. Since there are no $\alpha$-hydrogen atoms present, it cannot undergo keto-enol tautomerism. Thus, Statement II is false.

Answer: Statement I is true but Statement II is false