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Lecture11_Handout

# Lecture11_Handout - ¬ I assume ¬∃ x • P – use...

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Predicate Logic Summary of Additional Proof Strategies for Natural Deduction To show ¬∀ x P use proof by contradiction ( ¬ I), assume x P To show x P use forall introduction ( I) use proof by contradiction ( ¬ I), assume ¬∀ x P use exists elimination ( E) To show ¬∃ x P use proof by contradiction ( ¬ I), assume x P To show x P use exists introduction ( I)
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Unformatted text preview: ¬ I), assume ¬∃ x • P – use exists elimination ( ∃ E) • Generally, need to perform quantiﬁer elimination using ∀ E and ∃ E. Usually, the right order is to use ∃ E ﬁrst (ie, pick a formula of the form ∃ x • P and eliminate the quantiﬁer before picking a formula of the form ∀ x • P )....
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