Question

prepositional logic : For all is not perfect is equal to someone is not perfect or someone is perfect .

Comments

in propositional logic 'all students are not perfect' means there is at least someone who is not perfect.

 ∼(∀s P(s)) <=> ∃s ∼P(s)

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For all is not perfect is equal to someone is not perfect or someone is perfect .

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generally when we say 'some students are intelligent ' then by this we can't conclude that 'some students are not intelligent'. because it may happen that every student is intelligent so in that case some are subset of all , so eventually they would be intelligent is kind of 'trivial' conclusion. so here in this case we can't say some are not intelligent because we have already said every student is intelligent.

now come ot your question , it's given that 'every student is not perfect' ,this is basically negation of 'every student is perfect' and the result of this negation would mean , there would be at least some student who is not perfect. now the question is when we say , at least someone who is not perfect , does this means there is someone who is perfect?  NO you can't claim this because it may happen that every student is imperfect.

in gist we can say , some x are y doesn't mean some x are not y.