1.

For all a,b in R we define a*b =|a-b|Show tha t* commutative but not associative

Answer»

SOLUTION :(i) `FORALL` a,b in R we have
`a*b=|a-b|=|-(a-b)|=|b-a|=(b*a)`
`therefore`* Is commutative
we have
`(2*3)*4=|2-3|*4=|-1|*4=1*4=|1-4|=|-3|=3`
`therefore` (2*3)*4 ne 2 * (3*4)
Hence * is not associative


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