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Lecture Notes 7 CS1502

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Claire is at the library unless Max is home. B is a cube unless b is large. Why not for last two? ( section 7.3 and lecture) 8. Equivalences. P Q ... – PowerPoint PPT presentation

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Title: Lecture Notes 7 CS1502


1
Lecture Notes 7CS1502
  • Conditionals

2
Material Conditional
  • P?QP is called the antecedent and Q is called
    the consequent.

3
Definition of ?
4
(No Transcript)
5
English Translations
  • If P then Q
  • P implies Q
  • P only if Q
  • P is sufficient for Q
  • Q is necessary for P
  • Q if P

6
English Translation EGsP ? Q
  • If P then Q (If you are human then you are a
    mammal)
  • P implies Q (Being a human implies being a
    mammal)
  • If P, Q (If you are human, you are a
    mammal)
  • P only if Q (Youll live a long time only if
    you eat veggies)
  • P is sufficient for Q (Knowing youre living a
    long time is sufficient to know you eat veggies)
  • Q is necessary for P (Eating veggies is necessary
    to live a long time)
  • Q if P (You are a mammal if you are
    human)

7
?P ? Q
?Home(max) ? Library(claire) ?Large(b) ?
Cube(b) If not P then QIf Max is not home, then
Claire is at the library If b is not large,
then it is a cube Unless P, QUnless Max is at
home, Claire is at the library Unless b is
large, b is a cube Q, unless P Claire is at
the library unless Max is home B is a cube
unless b is large Why not ?? for last two?
(section 7.3 and lecture)
8
Equivalences
  • P ? Q
  • ?P ? Q
  • ?Q ? ?P

9
Biconditional
  • P ? Q
  • Equivalent to
  • (P ? Q) (Q ? P)

10
English Translations
  • P if and only if Q
  • P just in case Q

11
Truth Table for ?
12
Equivalencies
  • P ??Q
  • (P ? Q) ? (Q ? P)
  • (P ? Q) ? (?P ? ? Q)

P and Q are sufficient and necessary for each
other.
13
Well-formed Formula (wff)(updated definition)
  • Any atomic sentence is a wff.
  • If A are B are wffs then so are
  • ?A
  • A ? B
  • A ? B
  • A ? B
  • A ? B
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