I would say logic is a prerequisite for science. In other words science is specific application of logic, not something completely separate. Logic presents the next stage in the scientific process or thinking. So every logical thing can only be logical if its approved by a scientific method; (theory, hypothesis, e.t.c). One leads to another.
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Yes, Logic is now considered a branch of Science not of Philosophy anymore. In the old days Logic is formerly a branch of Philosophy.
There are allot of difference but the main difference is the science is discovered while the literature is invented
nothing.
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All science is knowledge but not all knowledge is science.