Originally Posted by
jenjen Hey, please helppp meeeeee....Thanks a lot in advance.
Algebraic Example: A will correspond to the squares on a chessboard, so that A= {1,2,3,4,5,6,7,8} X {1,2,3,4,5,6,7,8} and (x,y) will be related to (x',y') if and only if one of the quantities l x - x' l, l y - y' l is equal to 1 and the other is equal to 2. In nonmathematical terms this relation corresponds to the condition in chess that a knight positioned at square (x,y) is able to reach square (x',y') in one move provided the latter is not occupied by a piece of the same color.
Let R be the binary relation in Algebraic Example (the set is a chessboard, and the relation is that two squares are related if there is a knight's move from one to the other).
1) Let E be the equivalence relation generated by R. Show that E contains exactly one equivalence class; in other words, starting from the standard position on (1,2) the knight can reach every point on the chessboard.