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
What is the negation of the proposition, "A messaging package for a cell phone costs less than $20 per month."
a) A messaging package for a cell phone costs at least $20 per month.
b) A messaging package for a cell phone costs $20 per month.
c) A messaging package for a cell phone costs at most $20 per month.
d) A messaging more than $20 per month.
Answer is: a) A messaging package for a cell phone costs at least $20 per month.
Which is the "If ..., then ..." form of "It is hot whenever it is sunny"?
a) If it is not sunny, then it is hot.
b) If it is sunny, then it is hot.
c) If it is hot, then it is sunny.
d) If it is not sunny, then it is not hot.
Answer is: b) If it is sunny, then it is hot.
What is the converse of "If it snows today, I will ski tomorrow."
a) If I ski tomorrow then it snowed today.
b) If I do not ski tomorrow, then it will not have snowed 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: a) If I ski tomorrow then it snowed today.
The following is a proposition. True or False.
2 + 3 = x
Answer is: False
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 Thursday and it is cold"?
a) It is not Thursday and it is not cold.
b) It is not Thursday and it is cold.
c) It is not Thursday or it is cold.
d) It is not Thursday or it is not cold.
Answer is: d) It is not Thursday or it is not cold.
Let c be "it is cold" and r be "it is raining", which of the following is "It is rainy if it is not cold" in symbols?
a) ¬c ∧ r
b) ¬c ∨ d
c) r → ¬c
d) ¬c → r
Answer is: d) ¬c → r
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 "Al and Bill are absent"?
a) Al and Bill are present.
b) Al is present and Bill is not present.
c) Al is not present and Bill is present.
d) Either Al or Bill is present.
Answer is: d) Either Al or Bill is present.
Which is the "If ..., then ..." form of the statement "x is even only if y is odd"?
a) If x is not even, then y is odd.
b) If x is not even, then y is not odd.
c) If x is even, then y is odd.
d) If y is odd, then x is even.
Answer is: c) If x is even, then y is odd.
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.
Which is the contrapositive of "If ..., then ..." form of "The team wins if the quarterback can pass."?
a) If the team wins, then the quarterback can pass.
b) If the team does not win, then the quarterback cannot pass.
c) If the quarterback can pass, then the team wins.
d) If the quarterback cannot pass, then the team does not win.
Answer is: b) If the team does not win, then the quarterback cannot pass.
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 in the proper p → q format.
Whenever you get a speeding ticket, you are driving over 65 miles per hour.
a) d → s
b) d → ⌐s
c) s → d
d) ⌐s → d
Answer is: c) s → d
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.
The proposition p → q and its converse are logically equivalent.
Answer is: False
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