Propositions
The following is a proposition. True or False
"Answer this question now"
Answer is False. "Answer this question now" is a command.
If 3 = 1 + 1, then 3 = 2 + 2. True or False
Answer is: True
The negation of the proposition, "Some parrots are smart."
a) Some parrots are not smart.
b) All parrots are smart
c) Not all parrots are smart.
d) No parrots are smart.
Answer is: d) No parrots are smart.
If L(x, y): person x likes movie y. Domain for x is all people and for y is all movies. Then, write the following in good English.
EExEEyL(x,y)
Answer is: Someone does not like a movie.
What is the converse of "If it does not snow today, I will not ski tomorrow."
a) If I ski tomorrow then it snowed today.
b) If I do not ski tomorrow, then it did not snow today.
c) If it does not snow today, then I will not ski tomorrow.
d) If I ski tomorrow, then it did not snow today.
Answer is:b) If I do not ski tomorrow, then it did not snow today.
Which of the following is a proposition?
a) x2 - 5x + 2 > 0
b) Do not waste my time
c) There is life on Mars
d) What time is the exam
Answer is: c) There is life on Mars
Which of the following biconditionals are True?
a) 2 + 2 = 4 <=> 1 + 1 = 2
b) 1 + 1 = 2 <=> 2 + 3 = 4
c) 1 + 3 = 5 <=> 2 > 3
Answer is:
a) 2 + 2 = 4 <=> 1 + 1 = 2 and
c) 1 + 3 = 5 <=> 2 > 3
are True.
Which of the following is the negation of the statement "It is Friday and it is not cold"?
a) It is not Friday and it is not cold.
b) It is not Friday and it is cold.
c) It is not Friday or it is cold.
d) It is not Friday or it is not cold.
Answer is: c) It is not Friday or it is cold.
If L(x, y): person x likes movie y. Domain for x is all people and for y is all movies. Then, write the following in good English.
EEy L(John,y)
Answer is:There is at least one movie that John does not like.
What is the inverse of "I come to class only if there's a quiz."
a) If there is going to be a quiz, then I come to class
b) If do not come to class, then there is no quiz.
c) If there is not a quiz, then I do not come to class.
d) If I do not come to class then there's a quiz.
Answer is: b) If do not come to class, then there is no quiz.
is the inverse
How many inputs does the not operator have?
Answer is: One
Which of the following conditionals are True?
a) If 2 + 2 = 4 then 1 + 1 = 0
b) If 1 + 1 = 3 then 2 + 3 = 4
c) If 1 + 4 = 5 then 2 > 0
d) If the moon is made of cheese then my dog smells
Answer is:
b) If 1 + 1 = 3 then 2 + 3 = 4,
c) If 1 + 4 = 5 then 2 > 0 and
d) If the moon is made of cheese then my dog smells
are True
Which of the following is the negation of the statement AAx in RR, x^2 >= 0
a) EEx in RR, x^2 < 0
b) AAx in RR, x^2 < 0
c) EEx in ZZ, x^2 < 0
d) EEx in RR, x^2 <= 0
Answer is: a) EEx in RR, x^2 < 0
Which of the following is not correct (a) or (b)
a) notEEx(P(x)vvQ(x)-= AAx(notP(x)^^notQ(x))
b) EEx(P(x)^^Q(x))-=EEx(P(x)^^Q(x))
Answer is: b) EEx(P(x) ^^ Q(x)) -= EEx(P(x) ^^ Q(x))
What is the contrapositive of "It snows whenever the wind blows from the northeast."
a) If the wind blows from the northeast, then it snows.
b) If the wind does not blow from the northeast, then it does not snow.
c) If it snows, then the wind blows from the northeast.
d) If it does not snow, then the wind did not blow from the northeast.
Answer is: d) If it does not snow, then the wind did not blow from the northeast.
is the contrapositive
If it is snowing, then it is snowing. True or False.
Answer is: True
1 + 1 = 2 ^^ 1 + 1 = 3 <=> 2 + 2 = 3 vv 2 + 2 = 4. True or False
Answer is: 1 + 1 = 2 ^^ 1 + 1 = 3 <=> 2 + 2 = 3 vv 2 + 2 = 4
is False
The negation of "Some characters in the novel are doctors." is:
a) Some characters in the novel are not doctors.
b) No characters in the novel are doctors.
c) All characters in the novel are doctors.
d) There is at least one character in the novel that is a doctor.
Answer is: b) No characters in the novel are doctors.
To use proof by contraposition for all integers a and b, if a + b is odd, then a is odd or b is odd. Which of the following is true?
a) We assume not p is "a + b is odd"
b) We assume that not q is "a is even or b is even"
c) We assume that not q is "a is even and b is even"
Answer is: c) We assume that not q is "a is even and b is even"
Define: S1 = p vv q vv notp; S2 = p ^^ q ^^ not p; S3 = notp ^^ q
Which one of the following statements is TRUE if S1, S2, and S3 are as defined:
a)
S1 is a contradiction, S2 is a tautology and S3 is a contingency
a) S1 is a contradiction, S2 is a tautology and S3 is a contingency
b) S1 is a tautology, S2 is a contradiction and S3 is a contingency
c) S1 is a tautology, S2 is a contradiction and S3 is a tautology
d) S1 is a contradiction, S2 is a contingency and S3 is a tautology
Answer is: b) S1 is a tautology, S2 is a contradiction and S3 is a contingency
If a compound proposition has 4 propositions (e.g.: p ∧ q → r ∨ s), how many rows would the truth table for that proposition have?
Answer is: 24 = 16 rows
If 1 + 1 = 2 ^^ 1 + 1 = 3 then 2 + 2 = 3 vv 2 + 2 = 4. True or False
Answer is: If 1 + 1 = 2 ^^ 1 + 1 = 3 then 2 + 2 = 3 vv 2 + 2= 4
is True
The negation of "All characters in the play are children." is:
a) Some characters in the play are children.
b) Some characters in the play are not children.
c) It is not the case that all characters in the play are children.
d) All characters in the play are not children.
Answer is:
b) Some characters in the play are not children.
c) It is not the case that all characters in the play are children.
Assume that the universe for x is all people and the universe for y is the set of all movies. Let:
S(x, y) = person x saw movie y L(x, y) = person x liked movie y
What is the symbolic translation of:
There is some movie that Margaret saw but did not like.
a) EEy[S(Mary, y) ^^ notL(Mary, y)]
b) EEy[S(Mary, y) vv notL(Mary, y)]
c) AAy[S(Mary, y) ^^ notL(Mary, y)]
d) AAy[S(Mary, y) vv notL(Mary, y)]
Answer is a) EEy[S(Mary, y) ^^ notL(Mary, y)]
Let d and s be the propositions
d: You drive over 65 miles an hour
s: You get a speeding ticket
Write this proposition using d and s and logical connectives. "You drive over 65 miles per hour, but you do not get a speeding ticket."
a) s ∧ ⌐d
b) s → d
c) d → ⌐s
d) d ∧ ⌐s
Answer is d) d ∧ ⌐s