Represent with the language of First Order Predicate Logic the following proposition: "If S is an...

Represent with the language of First Order Predicate Logic the following proposition:

"If S is an arbitrary set of objects for which there is an associative binary operation * (function) with the following two properties: (1) for every pair of objects 'a' and 'b' from S there exists and object 'c' such that a * b = c (left solution property), then there exists in S an object 'e' such that e * x = x for all x in S (S has a left identity).

Expert Solution

ANSWER:

EXPLANATION:

All objects are in S. So the domain is taken to be S.

"For every pair of objects 'a' and 'b' from S there exists an object 'c' such that a * b = c" is written as

"There exists in S an object 'e' such that e * x = x for all x in S" is written as

Since there is a 'then' between the two sentences, we use the implies symbol

Colby Messinger answered 2 years ago

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