Final answer:
The statement about CH3CH₂COOH and C3H6O₂ being structural isomers is true. The false statement would likely be the assertion regarding the necessity of a double bond for cis-trans isomers, as cis-trans isomerism is specifically related to the spatial arrangement of substituents around a double bond.
Step-by-step explanation:
The statement "Molecules with the formulas CH3CH₂COOH and C3H6O₂ could be structural isomers" is true, so if presented as a false statement, it would be incorrect. Structural isomers have the same molecular formulas but different arrangements of atoms. Since both CH3CH₂COOH (propionic acid) and C3H6O₂ can represent more than one structure, it is feasible for them to be structural isomers, providing they have the same molecular formula but a different structural arrangement of atoms. For example, C3H6O₂ could be represented as propionic acid (CH3CH₂COOH) or as methyl acetate (CH3COOCH3).
The false statement among the given options would be that "Molecules must have a double bond to be cis-trans isomers" since cis-trans isomerism requires the presence of a double bond where the substituents can be either on the same side (cis) or opposite sides (trans) of the double bond.