problem set 1
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2/5/2014 Problem Set 1
https://courseworks.columbia.edu/samigo-app/jsf/delivery/beginTakingAssessment.faces 1/6
ProblemSet1
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Question 1 of 22 4.0 Points
Which of the following are propositions? (May choose multiple) A. Barack Obama was president of the United States in 2010.
B. Turn left and take three steps.
C. Twelve is a positive integer.
D. If Michael sleeps until noon, he will be late for class.
E. Are you hungry?
F. Neil Armstrong was the first human to walk on the moon.
G. Stop in the name of love.
Question 2 of 22 4.0 Points
Let p, q and r be the propositions
p : You get an A on the final exam q : You do every exercise in the book r : You get an A in this class
How would you best write the proposition "You get an A in this class, but you do not do every exercise in thebook"?
A. p r
B. r q
C. r q
D. r q
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Question 3 of 22 7.0 Points
Which choice is a valid simplification of the following compound statement:
[[[(p q) ^ r] [(p q) ^ r]] q] s
A. (p q) s
B. (p q) s
C. (p (q r)) s
D. (q r) s
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2/5/2014 Problem Set 1
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Question 4 of 22 4.0 Points
Given the following statements, choose the valid conclusion (and correct reason).
If Maria plays video games all afternoon, then she will not watch Netflix all evening.Maria watched netflix all evening ???
A. Maria did not watch Netflix all evening.
B. Maria did not play video games all afternoon.
C. Maria played video games all afternoon.
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Question 5 of 22 7.0 Points
Considerthefollowingargument: p(qr)psrs Andthefollowingflawedproof: StepsReason1.p(qr)Premise2.(pq)(pr)Step1andDistributivelaws3.(pr)Step2andSimplificationlaws4.psPremise5.psStep4andEquivalenceofconditionalanddisjunction6.rsSteps3&5andtheResolutionLaw Thereisoneerrorintheproof.Whichisit?
A. Left portion of step 3 should be "(p r)"
B. Reason of step 3 should be "Step 2 and Associative laws"
C. Left portion of step 5 should be "p s"
D. Reason of step 6 should be "hypothetical syllogism"
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Question 6 of 22 8.0 Points
Based on the following premises which of the conclusions are true (Select all that's true)
"If it's night ravens fly higher than falcons" "If it's day seahawks fly higher than eagles" "If it's night cardinals don't fly" "Eagles are flying higher than seahawks"
A. "Falcons are flying higher than ravens"
B. "Cardinals are flying"
C. "Ravens are flying higher than Falcons"
D. "Cardinals are not flying"
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2/5/2014 Problem Set 1
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Question 7 of 22 4.0 Points
Based on the following premises state whether the conclusion is correct or not
"All Jedi Grandmasters live for 900 years""Yoda lived for 900 years"
Conclusion "Yoda is a Jedi Grandmaster"
A. True
B. False
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Question 8 of 22 6.0 Points
Four of your friends make the following statements
Ann: One of us is lying.Ben: Two among us are lying.Carl: Three among us are lying.Dan: Four among us are lying.
Who's saying the truth?
(Hint if you cannot figure this out, try making a truth table...)
A. Ann
B. Ben
C. Carl
D. Dan
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Question 9 of 22 4.0 Points
Given that ( p q) is true, what can you conclude about the truth values of p and q?
A. At least one of p and q is false.
B. Exactly one of p and q is false.
C. Both p and q are false.
D. Neither p nor q is false
E. Cannot be determined
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Question 10 of 224.0 Points
If the statement q is false, what is the truth value of the statement: p (q r) ?
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2/5/2014 Problem Set 1
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A. Always true
B. Sometimes (or possibly) true
C. Never true (Always false)
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Question 11 of 22 4.0 Points
A (AB)
A. Always true
B. Sometimes (or possibly) true
C. Never true (Always false)
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Question 12 of 22 4.0 Points
(AB) B
A. Always true
B. Sometimes (or possibly) true
C. Never true (Always false)
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Question 13 of 22 4.0 Points
If A B, then (AB) B
A. Always true
B. Sometimes (or possibly) true
C. Never true (Always false)
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Question 14 of 22 4.0 Points
If (AB) = A, then (AB) = B
A. Always true
B. Sometimes (or possibly) true
C. Never true (Always false)
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Question 15 of 22 4.0 Points
If A B, then A (BA) = B
A. Always true
B. Sometimes (or possibly) true
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C. Never true (Always false)
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Question 16 of 22 4.0 Points
(A B) C = (A C) (B C)
A. Always true
B. Sometimes (or possibly) true
C. Never true (Always false)
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Question 17 of 22 4.0 Points
Negate the following statement: Everyone loves to mop.
A. At least one person loves to mop
B. At least one person does not love to mop
C. Some people love to mop
D. No one loves to mop
E. None of the above
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Question 18 of 22 4.0 Points
Negate the following statement: Some clowns are creepy.
A. All clowns are creepy
B. No clowns are creepy
C. At least one clown is not creepy
D. At least one clown is creepy
E. None of the above
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Question 19 of 22 4.0 Points
Negate the following statement: If she goes to rehab, she will be helped by Dr. Phil
A. If she doesnt go to rehab, she will not be helped by Dr. Phil
B. She goes to rehab and she is not helped by Dr. Phil
C. If she goes to rehab, then she will not be helped by Dr. Phil
D. She goes to rehab and she is helped by Dr. Phil
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2/5/2014 Problem Set 1
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E. None of the above
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Question 20 of 22 4.0 Points
Negate the following statement: The strike will end and TV will return to normal.
A. The strike will end and TV will not return to normal
B. The strike will not end or TV will return to normal
C. The strike will end and TV will return to normal
D. If the strike ends, then TV will return to normal
E. None of the above
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Question 21 of 22 4.0 Points
Negate the following statement: g h
A. g h
B. g h
C. g h
D. g h
E. None of the above
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Question 22 of 22 4.0 Points
Negate the following statement: p q
A. p q
B. p q
C. p q
D. p q
E. None of the above
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