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If n is not an odd integer then square of n is not odd. Let P(n) be the predicate that is not an odd integer, and (n) be the predicate that the square of n is not odd. For direct proof we should prove ○‡n : (P(n) ⇒ Q(n)) ○Vn : (P(n) ⇒ Q(n)) ○Vn : (¬P(n) ⇒ ¬Q(n)) ○³n : (¬P(n) ⇒ ¬Q(n)) Ovn: (¬Q(n) ⇒ ¬P(n))

If n is not an odd integer then square of n is not odd. Let P(n) be the predicate that is not an odd integer, and (n) be the predicate that the square of n is not odd. For direct proof we should prove ○‡n : (P(n) ⇒ Q(n)) ○Vn : (P(n) ⇒ Q(n)) ○Vn : (¬P(n) ⇒ ¬Q(n)) ○³n : (¬P(n) ⇒ ¬Q(n)) Ovn: (¬Q(n) ⇒ ¬P(n))

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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If n is not an odd integer then square of n is not odd. Let P(n) be the predicate that is not an odd integer, and (n) be the predicate that the square of n is not odd. For direct proof we should prove ○‡n : (P(n) ⇒ Q(n)) ○Vn : (P(n) ⇒ Q(n)) ○Vn : (¬P(n) ⇒ ¬Q(n)) ○³n : (¬P(n) ⇒ ¬Q(n)) Ovn: (¬Q(n) ⇒ ¬P(n))
Transcribed Image Text:If n is not an odd integer then square of n is not odd. Let P(n) be the predicate that is not an odd integer, and (n) be the predicate that the square of n is not odd. For direct proof we should prove ○‡n : (P(n) ⇒ Q(n)) ○Vn : (P(n) ⇒ Q(n)) ○Vn : (¬P(n) ⇒ ¬Q(n)) ○³n : (¬P(n) ⇒ ¬Q(n)) Ovn: (¬Q(n) ⇒ ¬P(n))
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