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Question: is the book states that the answer to this problem...

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is the relation β a partial order on the set S? For each partial order state whether it is weak or strong, total, or not totais

The book states that the answer to this problem is: Yes; strong; total

The answer I got is Irreflexive, Asymmetric, and Transitive which is wrong; can someone explain how can I get how can I get a strong partial order that's total?

My work so far:

I assumed that S = {a, b, c, d, e, ..., z}

I proved that it's not reflexive through: (d, d) being false because a letter cannot come before itself; which also means that it's Irreflexive

I think Antisymmetric is false because you can't have a letter that comes before itself and it can't be Symmetric either because of the order of the alphabet; so it has to be Asymmetric

It is transitive because (e,f) AND (f,k) -> (e,k) is true

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