An alkene that exhibits geometrical isomerism must have a carbon-carbon double bond, with each of the two carbons in the double bond attached to two different groups. Of the alkenes with formula C\(_4\)H\(_8\), only 2-butene exhibits geometrical isomerism:
\[\text{CH}_3 \text{CH} = \text{CHCH}_3.\]Oxidation of an alkene with KMnO\(_4\)/H\(^+\) cleaves the double bond, and converts each carbon in the double bond to a carbonyl group. Thus, Y is
\[\text{CH}_3 \text{COOH}.\]Heating the sodium salt of a carboxylic acid with a mixture of NaOH and CaO produces an alkane with one fewer carbon atom. This reaction is called the decarboxylation reaction. Thus, Z is CH\(_4\).