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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