(a) Draw the condensed structural formulas for the cis and trans isomers of 3-methyl-3-hexene. (b) Can cyclohexene exhibit cis-trans isomerism? Explain. (c) Does 2 -hexyne have geometric isomers? Explain.

First, let's start with drawing the parent chain of 6 carbons for hexene. The alkene (double bond) should be between carbons 3 and 4, and the methyl group should be attached to carbon 3. The cis and trans isomers can be drawn as follows: For the cis isomer: 1. Draw the parent chain with the double bond between carbons 3 (C3) and 4 (C4): \(CH_2=CH-CH_2-CH_2-CH_2-CH_3\) 2. Attach the methyl group to C3, placing it on the same side as the hydrogen on C4: \(CH_2=C(\text{H})CH(\text{CH}_3)-CH_2-CH_2-CH_3\) For the trans isomer: 1. Draw the parent chain with the double bond between carbons 3 (C3) and 4 (C4): \(CH_2=CH-CH_2-CH_2-CH_2-CH_3\) 2. Attach the methyl group to C3, placing it on the opposite side as the hydrogen on C4: \(CH_2=C(\text{CH}_3)CH(\text{H})-CH_2-CH_2-CH_3\)

To determine if cyclohexene can exhibit cis-trans isomerism, we need to check if there are two different groups on each carbon of the double bond. In cyclohexene, the double bond is between two carbons in a six-membered ring. Cyclohexene's structure is: \[CH_2=CH-CH_2-CH_2-CH_2-CH_2 \] Each carbon of the double bond is connected to one hydrogen and one carbon from the ring. Since each of these carbons has the same two groups attached to it (hydrogen and the rest of the ring), cis-trans isomerism is impossible in cyclohexene.

To determine if 2-hexyne has geometric isomers, we need to check the nature of the bond in its structure. The structure of 2-hexyne is: \[CH_3-C\equiv CH-CH_2-CH_2-CH_3 \] The bond between the second and third carbons (C2 and C3) is a triple bond (alkyne), which doesn't allow any rotation around the bond. Hence, 2-hexyne cannot have cis-trans (geometric) isomers since its structure is restricted by the triple bond.