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Consider the binary operations *: RxxR ...

Consider the binary operations `*: RxxR 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 `ast` is commutative but not associative, `o` is associative but not commutative.
Further, show that `AA a, b, in R, a*(b o c) = (a*b) o (a*c)`.

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It is given that `*: RxxR ->R` and `o: R xx R->R` defined as `a*b=|a-b|` and `a o b = a , AA a , b in R`.
For `a, b in R` , we have `a*b=|a-b|` and `b*a=|b-a|=|-(a-b)| = |a-b|`
`therefore a*b=b*a`
The `*` operation is commutative.
`(1*2)*3 = (|1-2|)*3 = 1*3 = |1-3|=2`
`1*(2*3) = 1*(|2-3|) = 1*1 = |1-1|=0`
`therefore (1*2)*3 ne 1*(2*3)`
The operation `*` is not associative. ...
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