Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

State whether the following statements are true or false. Justify.
(i) For an arbitrary binary operation * on a set N,  a * a = a ,  for all a * N.
(ii) If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a

Sagot :

crisforp
(i) false;
Let be N = { 0, 1 , 2}; x * y = x + y => a * a = 2a ∈ { 0, 2 , 4}, which is not a( just for a = 0);

(ii) true;
b * c = c * b => a * ( b * c ) = a * ( c * b );                  (1)
                   but, a * ( c * b ) = ( c *  b ) * a;               (2)

(1) and (2) => a * (b * c) = (c * b) * a.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.