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

Question

Mathematics

Whitie

10 October, 18:35

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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Greyson · Answer 1

(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.

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

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