We must first show tha a~a.

so is (a, b) ~ (a, b)?

That is, ab = ba? If you are doing multiplication (which I assume), then yes, that statement is true.

Now let's assume a ~ b. Show that b ~ a.

Since a ~ b, ad = bc. So cb = da, and thus, b ~ a.

Now you try transitivity. Assume that a ~ b and b ~ c. Try to show that a ~ c.

]]>S = {(a,b) ∈ Z x Z | b ≠ 0}. R is the relatoin on S defined by (a,b)R(c,d) if ad=bc.

Can anyone help? I'm completely lost.

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