s this ∃xQ(x) a tautology
Solution
The statement ∃xQ(x) is not a tautology. A tautology is a statement that is always true, regardless of the truth values of its components. The statement ∃xQ(x) is a quantified statement in predicate logic, which says "there exists some x such that Q(x) is true". This statement is not always true, because it depends on the specific interpretation of the predicate Q and the domain of discourse for x. If there is no x in the domain such that Q(x) is true, then the statement ∃xQ(x) is false. Therefore, ∃xQ(x) is not a tautology.
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