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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




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Topic review (newest first)

2006-03-24 15:36:09

Just take it one step at a time.

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.

2006-03-24 14:52:24

I need to prove that R is an equivalence relation S in the following:

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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