Let A={1,2,3,..,14,15}.Define the relation R on A*A (A squared) by(a,b)R(c,d) if a+d=b+c

find all the equivalence classes determined by R. represent the equivalence classes on the plane. what do the equivalence classes represent?

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- Mar 25th 2008, 01:39 AMmahu and lizdiscrete math
Let A={1,2,3,..,14,15}.Define the relation R on A*A (A squared) by(a,b)R(c,d) if a+d=b+c

find all the equivalence classes determined by R. represent the equivalence classes on the plane. what do the equivalence classes represent? - Mar 25th 2008, 05:48 AMtopsquark
Well, it's easy to find the equivalence classes.

Start with, say, (1, 1).

For another point (x, y) to be equivalent to this we require that 1 + y = 1 + x. So solve this for y and you get the equation y = x. Thus all the points in A X A that are equivalent to (1, 1) are in the form (a, a), where $\displaystyle a \in A$.

Now pick the point (2, 1), etc.

-Dan