Well, in this set up, we don't know anything about the relationship of odd and even, and we don't know anything about prime factorisations or that even means 'is divisible by 2 with no remainder'... The only premise here which is even related to even numbers and squares of even numbers is (1). — fdrake
I thought it was invalid because it seemed a lot like affirming the consequence to me. If you focus on the 2nd premise, — Ulrik
So the question becomes, can we conclude the statement: 'If the square of a number is even, then that number must be even' from the statement 'if a number is even, then its square must be even'? — fdrake
I thought this reasoning was invalid, but it is valid. — Ulrik
Either you understand what is written, or you don't. If you don't, then nothing more can be said. If you do, then you know what "odd" and "even" mean. (But then if you do, you don't really need to go through this logical exercise in order to prove the conclusion - you could prove it by other means.) — SophistiCat
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