CSE 2353

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CSE 2353 August 28th 2002

• Logic

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Propositions

• Def A statement which is True or False
• Which are Propositions
• This rose is white
• Keep off the grass
• 7 is even
• I am 6 years old
• A square has four sides
• Did you do your homework

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Operations

• And (conjunction)

p q pq
F F
F T
T F
T T
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Operations

• And (conjunction)
• Or (inclusive disjunction) v
• Xor (exclusive disjunction) v
• Not (negation) ?
• If then (implication) ? ?
• Iff (biconditional) ?
• Nand
• Nor ?
• Construct sentences with words

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Operations

• Other Operations

p q pq p v q p v q p ? q
F F F
F T F
T F F
T T T
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Precedence

• Precedence () v -gt ?
• (TvF)T ?
• Tv(FT) ?
• T v F T ?

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Operations
p q r p -gt (qr)
F F F
F T F
T F F
T T F
F F T
F T T
T F T
T T T
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Operations
p q r (p v q) ? r
F F F
F T F
T F F
T T F
F F T
F T T
T F T
T T T
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Tautologies andContradictions

• Tautology A statement which is True
• Contradiction
• p p
• p v p
• (pq) v (pq)
• p -gt p v q

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Practice

• Show that (p ? q ) implies p

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Practice

• Show that p v q is equivalent to (p q)
• Show that pp ? p
• Show that p ?q ? q ?p
• Show that (p q) r ? p (q r)
• Show that (p ? q) ? (p v q)

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Summary

• Propositions
• Operations on Propositions
• Truth Tables
• Precedence
• Tautologies and Contradictions

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Duality

• Swap t,f
• Swap ,v
• Example (p q) v p
• Dual (p v q) p
• If expressions are equivalent, so are duals

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Conditionals

• Given p ? q
• Converse q ? p
• Inverse p ? q
• Contrapositive q ? p

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Arguments

• If you insulted Bob then Ill never speak to you
  again. You insulted Bob so Ill never speak to
  you again.
• Premise
• Conclusion

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Arguments

• If you are a mathematician then you are clever.
  You are clever and rich. Therefore If you are
  rich then you are a mathematician.
• Premise
• Conclustion