What is the total number of isomers with the formula c3h6o that are either cyclic or chiral?

[SharkTank7]

I get all the isomers. There are four cyclic isomers and seven non-cyclic isomers.



According to Khan Academy, the answer for the total number of isomers with the formula c3h6o that are either cyclic or chiral is six. Four of them are the cyclic isomers: (R)-methyloxirane, (S)-methyloxirane, oxetane, and cyclopropanol. The other two are non-cyclic: (Z)-prop-1-en-1-ol and (E)-prop-1-en-1-ol.



My question is: why are these non-cyclic isomers considered chiral (since they're not cyclic, they must be chiral because the question asks for cyclic or chiral)?? There is no explanation whatsoever about this in Khan Academy. From my understanding of chirality, a molecule can be chiral in several ways. One of them is if it has a stereogenic center such as a carbon bonded to four different substituents. Clearly, these non-cyclic isomers don't satisfy this condition. Another way to be chiral is if it has an internal plane of symmetry. I am guessing that they do indeed have one, but I just can't seem to find it. Please help?



And there are five other isomers with the molecular formula c3h6o, that are not included in the answer, so I am assuming they must be achiral. How are these achiral as well??

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[Lawpy]

E/Z isomers are geometric isomers and a type of diastereomers that involve restricted rotation about the carbon-carbon double bond.

More information: Geometric Isomerism in Organic Molecules

I think Khan Academy is considering E/Z isomers and stereoisomers to be chiral. It's misleading because chirality should be strictly R/S isomers (i.e. enantiomers), since enantiomers are two mirror images that aren't superimposable, which is a defining property of chirality.