Ex 1.4, 12 State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation * on a set N, a * a = a a * N. Let us define * a * b = a + b Calculating a * a Let a = b = 2 So, a * a = 2 * 2 = 2 + 2 = 4 2 So, a * a a Therefore, statement is false. Ex 1.4, 12 State whether the following statements are true or false. Justify. (ii) If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a It is given that * is a commutative binary operation We need to check if a * (b * c) = (c * b) * a Solving R.H.S (c * b) * a = (b * c) * a = a * (b * c) = L.H.S. a * (b * c) = (c * b) * a Thus, statement is true.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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