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There are a lot of inconsistencies in the examples. For example, pumpkin pie is toast, but cheesecake, deep dish pizza, and key like pie are quiche.

An entire pumpkin pie or cheescake or deep dish pizza or key lime pie are all quiches.

A slice of any of them is a toast.

No inconsistency there.

Though I prefer "pizza" to "toast".

Simply, the cake is a quiche, but a slice is a toast.