1 / 18

Logic L3

Logic L3. i f p then q p --> q. Topics. Conditional proposition. Logical Equivalence. Converse. Bi-condition proposition. DEMorgan’s law for Logic. ASCII. Conversion: From Decimal to Binary from Binary to Decimal. Lab. Conditional P roposition & Logical Equivalence.

acton
Télécharger la présentation

Logic L3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Logic L3 if p then q p --> q

  2. Topics • Conditional proposition. • Logical Equivalence. • Converse. • Bi-condition proposition. • DEMorgan’slaw for Logic. • ASCII. • Conversion: • From Decimal to Binary • from Binary to Decimal. • Lab

  3. Conditional Proposition&Logical Equivalence • XYZ company declared to HCCC students if you graduate with a GPA >= 3.50 you will get a job at the company Proposition: if you graduate with a GPA >= 3.50 Proposition: you will get a job at XYZ company This proposition is called conditional proposition p: you graduate with a GPA >= 3.50 q: you will get a job at XYZ company p is called the hypotheses q is called the consequent or the conclusion Denoted as p -- q And read as if p then q

  4. Conditional proposition example 1 p: you graduate with a GPA >= 3.50 q: you will get a job at XYZ company • The Truth value of the conditional proposition p q is defined by the following table • When the hypothesis p is True then the conditional proposition p q is True if conclusion q is True. When the hypothesis p is True then the conditional proposition is False if conclusion q is False. When the hypothesis p is False then the conditional proposition is True regardless what q is. When the hypothesis p is False then the conditional proposition is True if conclusion q is False( Trur regardless what q is ). There is no reason to say that the statement is false if the hypothesis is false

  5. Conditional proposition example 2 • If you earn >= $70k/year you will be called a rich person. • p: you earn >= $70k/year. • q: you will be called a rich person.

  6. Conditional proposition example 2 p: you earn >= $70k/year.q: you will be called a rich person. • The Truth value of the conditional proposition p q is defined by the following table

  7. For all real number x, if x > 0, the X2>0 is True which means, no matter what number we replace x with, the result for p -> q will be True • Let p denote x >0 • Let q denote X2>0 p q x = 1 X2= 1 p is T q is T, p q is T p  q x = -2 X2= 4 p is F q is T, p q is T p  q x = 0 X2= 0 p is F q is F, p q is T p  q x > 0 to if X2 x will always be > 0, therefore q = f when p =T can never occur so p  q is F

  8. p q conclusion • p q is always True Except when p it True and q is False, in that case p  q is F

  9. p: 1 >2, q:4<8 • What is p  q • What is q  p Exercise: P is T, q is F, r is T (p ^ q)  r (p V q) ¬r p ^(q r) p (q  r)

  10. Converse • In ordinary language the hypothesis and conclusion in conditional proposition are normally related, but in logic the hypothesis and conclusion in conditional proposition are not required to be the same subject matter. • If 5 < 3 then nelson Rockefeller was the president of the US • The hypothesis is false so the proposition is True

  11. Converse • p:1 > 2, q: 4 < 8 • p  q F T is T • But • q  p T F is F We call the proposition q  p the CONVERSE of p q The conditional proposition can beTrue while the Converse is False

  12. Exercise • Write the converse symbolically and in words • If 1 < 2, then 3 < 6 • If 1>2, then 3 < 6

  13. Bi conditional Proposition • p if and only if q, iff • Compound composition (Proposition) • The statement is considered to be true PRECISLY when p and q have the same true value, both p and q are true. OR • Both p and q are false • If p and q are propositions, the compound proposition p if and only if q is called bi conditional proposition and is donated as p q

  14. Truth table for p iff q 1 < 5 if and only if 2 < 8 The statement 1 < 5 iff 2 <8 Can be written as p q 1<5 2<8 T T Then the statement is True

  15. DE Morgan LawLogically EQUIVALENCE • Two different compound propositions have the same truth values no matter what truth values their constituent propositions have, such propositions are said to be logically equivalent • The compound proposition 1<5 iff 2 <8 p iff q p q If they are both true or if they are both false then they are logically equivalent and denoted as p ≡ q

  16. p ≡ q ?? p v q ≡ p v q ?? p -> q ≡ p ʌ q ?? (p –>q) ʌ (q->p)

  17. ACCII Systems • American Standard Code for Interchange • Decimal Numbers base 10 • Binary numbers Base 2

  18. Numeric Conversion • Decimal to Binary conversion • Binary to Decimal conversion

More Related