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State whether the following statements are true or false. Justify. If star is a commutative binary operation on N, then a star (b star c) equals (c star b) star a

Q. 12State whether the following statements are true or false. Justify. 

(ii) If ∗ is a commutative binary operation on N, then a *(b*c) =( c*b)*a

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(ii) If ∗ is a commutative binary operation on N, then a *(b*c) =( c*b)*a

R.H.S  =(c*b)*a

            =(b*c)*a         (* is commutative)

           = a*(b*c)              (  as * is commutative)

             =    L.H.S

 \therefore          a *(b*c) =( c*b)*a

Hence, statement  (ii) is true.

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