Achiral and Chiral Compounds - B and D

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Compounds B and D lack chiral centers, but their chirality is determined by their symmetry. Compound B has a plane of symmetry, making it achiral, while compound D lacks this symmetry and is therefore chiral. The discussion emphasizes that the presence of chiral centers alone does not definitively classify a compound as achiral. Instead, the superimposability of mirror images is a more reliable criterion for determining chirality. Understanding these concepts is crucial for accurate classification of compounds in stereochemistry.
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Compounds B and D both have no chiralaty centers - but it seems to me that B has a plane of symmetry so it's achiral, and D has no plane of symmetry so it's chiral. I always thought though, that if a compound has no chiral centers then you can say with conffidence it's achiral. Is my analysis for B and D correct? And can you say anything with certeinty about a compound with no chiralaty centers?
 

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It's better to think in terms of superimposability of mirror images in these cases.
 
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