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Consider the binary opertions **: R xx R...

Consider the binary opertions `**: R xx R to R and o : R xx R to R` 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 opertion `**` distributes over the opertion 0]. Does o distribute over `**` ? Justify your answer.

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Step by step text solution for Consider the binary opertions **: R xx R to R and o : R xx R to R 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 opertion ** distributes over the opertion 0]. Does o distribute over ** ? Justify your answer. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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