Genmath Short Quiz 4 9. An implication is always logically equivalent to its
Name: ________________________________________ own contrapositive.
Part I: Instructions: At the back of the questionnaire write a. True
the letter of the correct answer in one column. (1pt each) b. False
1. Which of the following is a proposition? 10. Consider the following argument:
a. What time is it? If Tina spent the class funds on personal items, then
b. Read this carefully. she is guilty of a misdeed. Tina did spend the class
c. 1+3=2 funds on personal items. Therefore, she is guilty of a
d. X+1= 2 misdeed.
2. Which of the following sentences is a proposition a. Addition
whose truth value is T? b. Modus ponens
a. X+2=11 c. Modus tollens
b. Answer this question carefully. d. Hypothetical Syllogism
c. x+y =y+x for every pair of real numbers x 11. Consider the following argument:
and y If f(x) is a differentiable function, then it must be
d. 5+7 = 10 continuous. The function f(x) is not differentiable.
3. p^q is the proposition that is always true unless p Therefore, it is not continuous.
and q are false. What fallacy was used?
a. True a. Denying the hypothesis
b. False b. Affirming the conclusion
4. Let p and q be the proposition p: I will do every c. Begging the question or Circular reasoning
exercise in the book and q: I will get a perfect score 12. Consider the following argument:
in this test. Which of the following corresponds to It is either hotter than 37 degrees today or the
the proposition “Either I will get a perfect score in pollution level has reached critical level. It is less
this test or I will not do every exercise in the book”? than 37 degrees today. Therefore, the pollution has
a. q^p reached critical level.
b. ¬ q ^ ¬ p What rule of inference was used?
c. ¬ p v q a. Simplification
d. ¬ p ⇒¬ q b. Modus ponens
5. Let p, q, and r be the propositions p: You get a c. Modus tollens
perfect score in the final exam, q: You do every d. Disjunctive syllogism
exercise in the book, and r: You get the highest 13. Consider the following argument:
grade in this class. Which of the following If I work all night on the end-of-chapter exercises,
corresponds to the proposition “You will get the then I can answer all the items in the problem set. If
highest grade in this class if and only if you either do I answer all the exercises, I will understand the
every exercise in the book or you get a perfect score entire chapter. Therefore, if I work all night on the
in the final exam”? end-of-chapter exercises, then I will understand the
a. p ⇔(q ∨r ) entire chapter.
b. p ⇔(q ∨ p) Which rule of inference was used?
c. r ⇒( p ∨ q) a. Modus ponens
d. (q ∨ p) ⇔r b. Hypothetical syllogism
6. A compound proposition that is always false, no c. Modus Tollens
matter what the truth values of the propositions d. Disjunctive Syllogism
that occurs in it are, is called a________. 14. The following is a proof that n2 is odd if n is odd:
a. Tautology Let n=2 k +1. Then
2 2 2 2
b. Contradiction n =( 2 k+ 1 ) =4 k +4 k +1=2 ( 2 k +2 k ) +1.Thus,
c. Contingency 2
n is odd.
d. Fallacy What kind of proof was used?
7. What is the contrapositive of the implication “I a. Direct proof
come to class whenever there is going to be an b. Indirect proof
examination”? c. Proof by cases
a. If I come to class, then there will be an 15. The following is a proof that the sum of two odd
examination. integers n and m is even:
b. If I do not come to class, then there will not Let n=2 k +1 and m=2 l+1 be odd integers. Then,
be an examination. n+ m=( 2 k +1 )+ ( 2l+1 )=2k + 2l+2=2(k +l+1) is
c. If there will not be an examination, then I even.
come to class. What kind of proof was used?
d. If there will not be an examination, then I a. Direct proof
do not come to class. b. Indirect proof
8. Let p and q be the compound propositions p: If n is c. Proof by cases
2
Name: ________________________________________ own contrapositive.
Part I: Instructions: At the back of the questionnaire write a. True
the letter of the correct answer in one column. (1pt each) b. False
1. Which of the following is a proposition? 10. Consider the following argument:
a. What time is it? If Tina spent the class funds on personal items, then
b. Read this carefully. she is guilty of a misdeed. Tina did spend the class
c. 1+3=2 funds on personal items. Therefore, she is guilty of a
d. X+1= 2 misdeed.
2. Which of the following sentences is a proposition a. Addition
whose truth value is T? b. Modus ponens
a. X+2=11 c. Modus tollens
b. Answer this question carefully. d. Hypothetical Syllogism
c. x+y =y+x for every pair of real numbers x 11. Consider the following argument:
and y If f(x) is a differentiable function, then it must be
d. 5+7 = 10 continuous. The function f(x) is not differentiable.
3. p^q is the proposition that is always true unless p Therefore, it is not continuous.
and q are false. What fallacy was used?
a. True a. Denying the hypothesis
b. False b. Affirming the conclusion
4. Let p and q be the proposition p: I will do every c. Begging the question or Circular reasoning
exercise in the book and q: I will get a perfect score 12. Consider the following argument:
in this test. Which of the following corresponds to It is either hotter than 37 degrees today or the
the proposition “Either I will get a perfect score in pollution level has reached critical level. It is less
this test or I will not do every exercise in the book”? than 37 degrees today. Therefore, the pollution has
a. q^p reached critical level.
b. ¬ q ^ ¬ p What rule of inference was used?
c. ¬ p v q a. Simplification
d. ¬ p ⇒¬ q b. Modus ponens
5. Let p, q, and r be the propositions p: You get a c. Modus tollens
perfect score in the final exam, q: You do every d. Disjunctive syllogism
exercise in the book, and r: You get the highest 13. Consider the following argument:
grade in this class. Which of the following If I work all night on the end-of-chapter exercises,
corresponds to the proposition “You will get the then I can answer all the items in the problem set. If
highest grade in this class if and only if you either do I answer all the exercises, I will understand the
every exercise in the book or you get a perfect score entire chapter. Therefore, if I work all night on the
in the final exam”? end-of-chapter exercises, then I will understand the
a. p ⇔(q ∨r ) entire chapter.
b. p ⇔(q ∨ p) Which rule of inference was used?
c. r ⇒( p ∨ q) a. Modus ponens
d. (q ∨ p) ⇔r b. Hypothetical syllogism
6. A compound proposition that is always false, no c. Modus Tollens
matter what the truth values of the propositions d. Disjunctive Syllogism
that occurs in it are, is called a________. 14. The following is a proof that n2 is odd if n is odd:
a. Tautology Let n=2 k +1. Then
2 2 2 2
b. Contradiction n =( 2 k+ 1 ) =4 k +4 k +1=2 ( 2 k +2 k ) +1.Thus,
c. Contingency 2
n is odd.
d. Fallacy What kind of proof was used?
7. What is the contrapositive of the implication “I a. Direct proof
come to class whenever there is going to be an b. Indirect proof
examination”? c. Proof by cases
a. If I come to class, then there will be an 15. The following is a proof that the sum of two odd
examination. integers n and m is even:
b. If I do not come to class, then there will not Let n=2 k +1 and m=2 l+1 be odd integers. Then,
be an examination. n+ m=( 2 k +1 )+ ( 2l+1 )=2k + 2l+2=2(k +l+1) is
c. If there will not be an examination, then I even.
come to class. What kind of proof was used?
d. If there will not be an examination, then I a. Direct proof
do not come to class. b. Indirect proof
8. Let p and q be the compound propositions p: If n is c. Proof by cases
2
