Pls solve 11

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a * b = a + b - ab . . . (i) Commutative : b * a = b + a - ba \Rightarrow b * a = a + b - ab . . . (ii) by (i) and (ii) Hence * is commutative Now Asscociative (a * b) * c = (a + b - ab) * c = a + b - ab + c - (a + b - ab) c (a * b) * c = a + b + c - ab - bc - ca + abc . . . (iii) a * (b * c) = a * (b + c - bc) = a + b + c - bc - a (b + c - bc) a * (b * c) = a + b + c - ab - bc - ca + abc . . . (iv) By (iii) and (iv) (a * b) * c = a * (b * c) Hence * is accociative . As * is commutative and associative, hence * is a binary operation . Let e be the identity element, then a * e = e = e * a \Rightarrow a + e - ae = e \Rightarrow a - ae = 0 \Rightarrow a (1 - e) = 0 \Rightarrow 1 - e = 0 \Rightarrow e = 1 Hencen operation is not defined for 1 . Hence there exist no identity element .

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