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Question : 11
Total: 29
(i) Is the binary operation *, defined on set N, given by a * b =
(ii) Is the above binary operation * associative?
(ii) Is the above binary operation * associative?
Solution:
(i) For all a , b ∊ N , a * b =
Now , b * a =
Thus, the binary operation * is commutative.
(ii) Let a , b , c ∊ N
a * b * c = a *(
)
a * b * c =(
)
∴ a * b * c ≠ a * b * c
Thus, the binary operation * is not associative.
Now , b * a =
Thus, the binary operation * is commutative.
(ii) Let a , b , c ∊ N
a * b * c = a *
a * b * c =
∴ a * b * c ≠ a * b * c
Thus, the binary operation * is not associative.
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