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Consider the binary operations ** R xx R rarrR and o : RxxR rarrR defined as a**b |a-b| and " a o b " = a, AA a , b in R . Show that ** is commutative but not associative , o is associative but not commutative. Further, show that AA a , b ,c in R , a ** ("b o c")= (a**b) o (a**c) . [If it is so , we say that the operation ** distributes over the operation o] . Does o distribute over ** ? Justify your answer. |
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