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Adv Alegbra HW Solutions 49

Adv Alegbra HW Solutions 49 - 49 2.36 True or false with...

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49 2.36 True or false with reasons. (i) The function e : N × N N , de fi ned by e ( m , n ) = m n , is an associative operation. Solution. False. (ii) Every group is abelian. Solution. False. (iii) The set of all positive real numbers is a group under multiplication. Solution. True. (iv) The set of all positive real numbers is a group under addition. Solution. False. (v) For all a , b G , where G is a group, aba 1 b 1 = 1. Solution. False. (vi) Every permutation of the vertices v 1 , v 2 , v 3 of an equilateral trian- gle π 3 is the restriction of a symmetry of π 3 . Solution. True. (vii) Every permutation of the vertices v 1 , v 2 , v 3 , v 4 of a square π 4 is the restriction of a symmetry of π 4 . Solution. False. (viii) If a , b G , where G is a group, then ( ab ) n = a n b n for all n N
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