Chirality Questions - Need Answers Checked

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The discussion revolves around the correctness of answers related to chirality and isomerism. The first statement about constitutional isomers being chiral is affirmed as true, while the second statement about every chiral compound having a diastereomer is also true. The third statement is corrected, as diastereomers are not mirror images of each other, making it false. The fourth statement is true, as a lack of a plane of symmetry indicates chirality. The fifth statement is false because compounds without a chiral center can still possess diastereomers, such as sp2 hybridized molecules.
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I had to answer true or false for the following five questions. If they were false, I had to explain why.

1. In some cases, constitutional isomers are chiral. TRUE
2. Every chiral compound has a diastereomer. TRUE
3. Some diastereomers have mirror-image relationship. FALSE
Diastereomers are not mirror images of each other.
4. If a structure has no plane of symmetry it is chiral. TRUE
5. If a compound has a diastereomer it must be chiral. FALSE
Compounds without a chiral center (like an sp2 hybridized molecule) can have a diastereomer.

So I need to know if my answers are correct. If not, why are my answers (if any) incorrect? Thanks.
 
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Skimming your answers, no guarantee, but they look good.
 
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