Lecture Notes 7 CS1502

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Lecture Notes 7CS1502

• Conditionals

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Material Conditional

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

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Definition of ?
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(No Transcript)
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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

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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)

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?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)
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Equivalences

• P ? Q
• ?P ? Q
• ?Q ? ?P

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Biconditional

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

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English Translations

• P if and only if Q
• P just in case Q

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Truth Table for ?
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Equivalencies

• P ??Q
• (P ? Q) ? (Q ? P)
• (P ? Q) ? (?P ? ? Q)

P and Q are sufficient and necessary for each
other.
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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