In accordance with propositional logic, quantifier theory and definitions of simple and composite propositions, the negation of a implication has the following equivalence:
[tex]\neg (\exists \,x\, (P(x) \implies Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))[/tex] (Correct choice: iii)
How to find the equivalent form of a proposition
Herein we have a composite proposition, that is, the union of monary and binary operators and simple propositions. According to propositional logic and quantifier theory, the negation of an implication is equivalent to:
[tex]\neg (\exists \,x\, (P(x) \implies Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))[/tex]
To learn more on propositions: https://brainly.com/question/14789062
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