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