Discussion
The axiom of excluded middle is represented as :
Answer: A
The law of excluded middle is A ∪ \(\overline{\text{A}}\) = X.
For a classical (crisp) set A in the universe X, every element is either in A or in its complement, so the union of A and its complement is the whole universe. Its partner, the law of contradiction, says A ∩ \(\overline{\text{A}}\) = ∅, since nothing is in both.
A ∩ \(\overline{\text{A}}\) = X confuses the two laws, and the options built only from \(\overline{\text{A}}\) reduce to \(\overline{\text{A}}\) = X, which holds only for an empty A. In fuzzy set theory both laws fail in general, which is one of the distinguishing points of fuzzy sets.
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