1.

Show that * on R-{-1} defined by (a*b) =(a)/(b+1) is neither commutative nor associative

Answer»

Solution :(i)` 2*3=(2)/(3+1)=2/4=1/2and 3*2=(3)/(2+1)=3/3=1`
`therefore 2*3 NE 3*32` so * is not ocmmutative
(II) `(2*3)*1=1/2*1=(1//2)/(1+1)=1/4`
`(3*3)=(3)/(1+1)=3/2 `
`therefore 2*(3*1)=2*3/2=(2)/(3/2+1)=(2xx2/5)=4/5`
Thus (2*3)*1 ne 2*(3*1)


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