plz ans this 28th question
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In mathematical algebra a semigroup is a set of elements with an operation (function) defined on the set. The function needs to be associative function for all elements of the set. It may not be commutative.
Given set = N = set of natural numbers.
Operation = * such that *(a,b) = a * b = a^b ie. exponentiation.
Clearly, a * (b * c) is not equal to (a * b) * c
As a^ (b^c) not equals (a^b)^c = a^(bc) for all a,b, c € N .
This will be true only if bc = b^c ie. for b = 0 or for c = 1 or for c = b^{c-1}.
Example
(2 * 3) * 4 = 2^12
2 * (3 * 4) = 2^81
They aren't equal.
Given set = N = set of natural numbers.
Operation = * such that *(a,b) = a * b = a^b ie. exponentiation.
Clearly, a * (b * c) is not equal to (a * b) * c
As a^ (b^c) not equals (a^b)^c = a^(bc) for all a,b, c € N .
This will be true only if bc = b^c ie. for b = 0 or for c = 1 or for c = b^{c-1}.
Example
(2 * 3) * 4 = 2^12
2 * (3 * 4) = 2^81
They aren't equal.
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hope this helps you
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