CS 486, Spring ’01
February 1, 2001
10 questions
Quiz 1
- degree (((p Ú q) & r) É q)) = 4
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false
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- In any tree, finite or infinite, each point
has only finitely many
predecessors.
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true
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- Circle each line which is not a
subformula of ((p Ú q) & r) É (q & r)
(perhaps all are or none are)
a. (p Ú q)
b. r
c. q
d. (q & r)
e. r É q
CORRECT ANSWER
- The truth table for ((p Ú q) & r) É (q & r) has this number of rows:
- 22 = 4
- 23 = 8 CORRECT ANSWER
- 25 = 32
- 33 = 27
- A formula X is called satisfiable iff
~X is true in at least one
Boolean valuation
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false
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- left : A + right : B = right : B + left : A
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true
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- ((study implies goodgrades) and not(goodgrades)) implies
not(study)
is a true fact of psychology but not a tautology (logically true)
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false
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- Every propositional formula is truth
functionally equivalent to either t or f
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false
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- Circle the best among these translations of $X:Form.(X = p1)
- all formulas contain p1
- p1 is a formula
- some formula is p1 CORRECT ANSWER
- no formula is p1
- Circle all statements that are in our
metalanguage
- " X : Form.(X = p1 or
not(X = p1))
CORRECT ANSWER
- (p1 Ú p2)
- (p1 É p1) is a tautology CORRECT ANSWER
- (p1 É (p2 É p1))