Showing they exist is easy enough; there are only finitely many functions, each expression takes on one such function for each of the possible operators, so the total is still finite. Since there are infinitely many such expressions, some of them must be the same. Actually finding similar equations for more letters is also easy. If f(A) = g(A), then f(A)B = g(A)B, etc. For systems with more than 2 elements, the size of the required expression probably grows exponentially. Ditto for operators on more than 2 operands. Franklin T. Adams-Watters -----Original Message----- From: rcs@CS.Arizona.EDU Universal Equation Is there an equation that is true for all 2-element binary operators? (Besides A=A. :-)) PDP10 aficionados will recall the 16 boolean instructions (ANDCA, etc.). There are 10 non-isomorphic tables, or 7 if we allow argument swapping. (Zero, Left, And, Xor, Nor, ~Left, Andcm.) All of them satisfy the identity A:.A.AA:A = A:.AA.A:A or A{[A(AA)]A} = A{[(AA)A]A}. Puzzle: Show that similar equations exist with more letters, and for systems with more than 2 elements, and for ternary operators (tragmas). Problem: Find some. ________________________________________________________________________ Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection.