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bogdanovich [222]
1 year ago
8

Find the negation of the proposition

Mathematics
1 answer:
murzikaleks [220]1 year ago
8 0

In accordance with <em>propositional</em> logic, <em>quantifier</em> theory and definitions of <em>simple</em> and <em>composite</em> propositions, the negation of a implication has the following equivalence:

\neg (\exists \,x\, (P(x) \implies  Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x)) (Correct choice: iii)

<h3>How to find the equivalent form of a proposition</h3>

Herein we have a <em>composite</em> proposition, that is, the union of <em>monary</em> and <em>binary</em> operators and <em>simple</em> propositions. According to <em>propositional</em> logic and <em>quantifier</em> theory, the negation of an implication is equivalent to:

\neg (\exists \,x\, (P(x) \implies  Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))

To learn more on propositions: brainly.com/question/14789062

#SPJ1

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