When can we say a set is a group with an operand *?
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which holds the commudative law
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which holds associative law
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there exist an identity element and inverse for all elements in a set.
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All the above
A group requires four axioms: closure, associativity, identity element existence, and inverse element existence for all elements. Option D correctly states that all these properties must hold. Commutativity alone (option A) makes it an abelian group but is not required for a basic group. Associativity (option B) and identity/inverse (option C) are necessary but not sufficient alone.
A group must satisfy associativity, have an identity element, and have inverses for every element. Commutativity is not strictly required (a group with commutativity is called abelian), but a set that satisfies all of the listed properties is certainly a group. Since none of the single options alone is enough to guarantee a group, 'All the above' is the correct choice.