Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields 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 dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.