(a) 4 -chloro- 1 -methylcyclohexane (b) trans 4 -chloro- 1 -methylcyclohexane (c) trans 1 -chloro-4-methylcyclohexane (d) trans 1 -methyl-4-chlorocyclohexane

In order to correctly identify the correct name for the given molecule, first, know the functional groups present. In this case, they are a methyl group (CH3) and a chloro group (Cl). Step 2: Understand the 'trans' prefix

The prefix 'trans' refers to the geometric isomerism. In the given exercise, we are dealing with cyclohexane. The 'trans' prefix indicates that the two functional groups (methyl and chloro) are present on the opposite side of the cyclohexane ring, meaning in axial and equatorial positions. Step 3: Correctly number the positions on the cyclohexane ring

Numbering the positions on cyclohexane starts from the first carbon attached to the first functional group and proceeds in such a way to give the lowest numbering to the functional groups. Both the methyl and chloro groups should be present on opposite sides and as close as possible to follow the 'trans' nomenclature. Now let's analyze each given name: (a) 4 -chloro- 1 -methylcyclohexane: This name implies that the Cl group is in the 4th position and the methyl group is in the 1st position, which is a correct numbering, but it doesn't provide information about the axial or equatorial orientation of the functional groups, so it cannot be considered as 'trans'. (b) trans 4 -chloro- 1 -methylcyclohexane: This name implies that the Cl group is in the 4th position and the methyl group is in the 1st position, with both functional groups present on the opposite side, which follows the 'trans' nomenclature. This is the correct name for the given molecule. (c) trans 1 -chloro-4-methylcyclohexane: This name implies that the Cl group is in the 1st position and the methyl group is in the 4th position, with both functional groups present on the opposite side, which also follows the 'trans' nomenclature. However, this is an incorrect numbering because the numbering should start from the carbon attached to the first functional group (CH3). (d) trans 1 -methyl-4-chlorocyclohexane: This name is similar to the previous one, but it has reversed the position of the functional groups chloride and methyl. This is again an incorrect numbering. Thus, the correct IUPAC name for the given molecule is:

trans 4 -chloro- 1 -methylcyclohexane