2/5/2014 Problem Set 1

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Problem Set 1

Part 1 of 1 ­

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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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

Consider the following argument: p ∨ (q ∧ r)p → s          ∴ r ∨ s And the following flawed proof:  Steps                        Reason1. p ∨ (q ∧ r)               Premise2. (p ∨ q) ∧ (p ∨ r)         Step 1 and Distributive laws3. (p ∧ r)                   Step 2 and Simplification laws4. p → s                      Premise5. ¬p ∨ s                    Step 4 and Equivalence of conditional and disjunction6. ∴ r ∨ s                   Steps 3 & 5 and the Resolution Law There is one error in the proof. Which is it?

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 sea‐hawks fly higher than eagles" "If it's night cardinals don't fly" "Eagles are flying higher than sea‐hawks"

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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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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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 ⊆ (A∩B)

A. Always true

B. Sometimes (or possibly) true

C. Never true (Always false)

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Question 12 of 22 4.0 Points

(A∩B) ⊆ 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 (A∪B) ⊆ 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 (A∩B) = A, then (A∪B) = 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 ∪ (B−A) = 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 doesn’t 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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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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