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# Check the commuta

Given that * is a binary operation on R defined by a*b = a + b – 7 for all a,bR.

We know that commutative property is p*q = q*p, where * is a binary operation.

Let’s check the commutativity of given binary operation:

a*b = a + b – 7

b*a = b + a – 7 = a + b – 7

b*a = a*b

Commutative property holds for given binary operation * on R.

We know that associative property is (p*q)*r = p*(q*r)

Let’s check the associativity of given binary operation:

(a*b)*c = (a + b – 7)*c

(a*b)*c = a + b – 7 + c – 7

(a*b)*c = a + b + c – 14 ...... (1)

a*(b*c) = a*(b + c – 7)

a*(b*c) = a + b + c – 7 – 7

a*(b*c) = a + b + c – 14 ...... (2)

From (1) and (2) we can clearly say that associativity holds for the binary operation ‘*’ on ‘R’.

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