SAMPLE TRUE OR FALSE QUESTIONS
Answers: 1-T, 2-T, 3-F, 4-F, 5-F
- The intersection of two disjoint sets has no proper subsets.
TF
2.If a quarter is worth less than two dimes, then a dollar is worth less than two quarters.
TF
3.Anycircuit representing a tautology is always open (i.e. its light bulb is always OFF when electricity flows through the circuit).
TF
4.If an argument has premises that are all false, then it is invalid.
T F
5. if and only .
T F
SAMPLE MULTIPLE-CHOICE QUESTIONS
Answers: 6-B, 7D, 8-C, 9-B
6.The statement “I won’t go to the beach whenever I read about oil spills” is equivalent to which of the following statements?
a)IfI don’t read about oil spills, I’llgo to the beach.
b)I don’t read about oil spills whenever I go to the beach.
c)I go to the beach whenever I don’t read about oil spills.
7.If an Italian restaurant offers 5 different toppings to put on their pizzas, how many different pizzas can the restaurant prepare?
Note:Assume therestaurant also prepares pizzas with no toppings.
a)16b)25
c)31d)32
8.The negation of the statement “No one is safe from making a logical fallacy sometimes” is given by
a)Everyone is safefrom making a logical fallacy sometimes.
b)Everyoneis safe from making a logical fallacy all the time.
c)Someone is safe from making a logical fallacy sometimes.
d)Someone is not safe from making a logical fallacy sometimes.
e)Someone is not safe from making a logical fallacy all the time.
9.The number of rows in the truth table for the compound statement is given by
a)8b)16
c)32d)64
Sample Problem 1
Paula is a big fan of the great 20th-century Russian composers.
Examining her collection of24albums, a quick survey found the following:
Paula has 5 albums that feature compositions by both Stravinsky and Prokofiev.
Paula has 6 albumsthat only feature compositions by Stravinsky.
Paula has 7 albums that feature compositions by Prokofiev.
Summarize the results of this survey using aVenn diagramin the space provided below.
Now answer the following questions:
a)How many albumsin Paula’s collectiononly feature compositions by Prokofiev?
Answer: 2
b)How many albums albums in Paula’s collection feature no compositions by either Stravinsky or Prokofiev?
Answer: 11
Sample Problem 2
Answer: follow the same procedure as in Sample Problem 2 for Exam 1
Use the Venn diagram below to show that
.
For your convenience, the 8 regions in the diagram have been numbered arbitrarily.
Sample Problem 3
Answer: valid by Modus Tollens
Consider the following argument:
“If I write a check,it will bounce; but the check will not bounce whenever the bank guarantees my check. The bank decides to guarantee my check. Therefore, I decide not to write a check.”
a)Write this argument in symbolic form using, and as its component statements. Start by writing these three components explicitly.
b)Use the truth table below to determineif this argument is validor not.
Note: You may bypass the construction of the table if you recognize a standard forms after manipulating the premises symbolically.
p / q / rT / T / T
T / T / F
T / F / T
T / F / F
F / T / T
F / T / F
F / F / T
F / F / F
Sample Problem 4
Answer: “If and n is even, then n is not prime.”
Write the contrapositive of the conditional statement below.
“ is a prime number implies that or is an odd number.”
Your answer must contain a conjunction in its premise.
Sample Problem 5
Show that the statement is a logical contradiction.
Here you may use a truth table, symbolic manipulation, or circuits to justify your answer.
Sample Problem6
Answer (one of many):
Finda set expression that corresponds to the shaded region shown in the Venn diagram below.
Sample Bonus Problem 1
Answer: see problem 3 for circuits in Take-Home Exam 3
Draw the circuit corresponding to the statement , the negation of the biconditional statement “if and only if .”
Sample Bonus Problem 2
Answer: 16
If aset has 16 elements, another set has 17 elements and a third set has 7 elements, then what is the maximum possible number of elements in the set ?
Sample Bonus Problem 3
Answer: fallacy of the inverse
Show the fallacy of the symbolic argument given below withoutresorting to a truth table.
(premise 1)
(premise 2)
(premise 3)
______
(conclusion)