a reaj to 5 × ab reaj to 5 = ab reaj to 5
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Solution:
For Commutative
Given. a* b = 1 + ab
Now, b * a = 1 + ba = 1 + ab
∴ a*b = b*a
So. it is commutative .
For Associative
(a* b)*c = (1+ab)*c
= 1 + (1 + ab) c
= 1 + c + abc
and a*(b*c)=a*(1 + bc)
= 1 + a(1 + be)
= 1 + a + abc
(a* b)*c ≠ a*(b*c)
So, it is not associative .
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