2-2 Logic of Compound Statement III_수정.ppt - Logic of Compound Statement III Prof Anand Paul Tautology and Contradiction • A tautology is a

2-2 Logic of Compound Statement III_수정.ppt - Logic of...

This preview shows page 1 - 9 out of 22 pages.

Logic of Compound Statement III Prof. Anand Paul
Image of page 1

Subscribe to view the full document.

A tautology is a statement that is always true p ¬p will always be true (Negation Law) A contradiction is a statement that is always false p ¬p will always be false (Negation Law) p p ¬ p p ¬ p T T F F T F Tautology and Contradiction
Image of page 2
A logical equivalence means that the two sides always have the same truth values Symbol is ≡ or We’ll use ≡, so as not to confuse it with the bi-conditional Logical Equivalence
Image of page 3

Subscribe to view the full document.

p T ≡ p Identity law p F ≡ F Domination law p T p T T T T F T F p F p F T F F F F F Logical Equivalences of And
Image of page 4
p p ≡ p Idempotent law p q ≡ q p Commutative law p p p p T T T F F F p q p q q p T T T T T F F F F T F F F F F F Logical Equivalences of And
Image of page 5

Subscribe to view the full document.

(p q) r ≡ p (q r) Associative law p q r p q (p q) r q r p (q r) T T T T T T T T T F T F F F T F T F F F F T F F F F F F F T T F F T F F T F F F F F F F T F F F F F F F F F F F Logical Equivalences of And
Image of page 6
p T ≡ T Identity law p F ≡ p Domination law p p ≡ p Idempotent law p q ≡ q p Commutative law (p q) r ≡ p (q r) Associative law Logical Equivalences of Or
Image of page 7

Subscribe to view the full document.

(p q) r ≡ p q r (p q) r ≡ p q r Similar to (3+4)+5 = 3+4+5 Only works if ALL the operators are the same!
Image of page 8
Image of page 9
  • Winter '16
  • Yoo Ki Young

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask bonus questions You can ask questions ( expire soon) You can ask questions (will expire )
Answers in as fast as 15 minutes