hannaho64
20.08.2019 •
Mathematics
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
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Ответ:
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.
Ответ:
The first one
Step-by-step explanation:
I drew it with my graphic calculator.