sec 1.1
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You get an A on the final exam.q: You do every exercise in this book.r: You get an A in this class. Identify the expression for the proposition "Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class" using p, q, and r and logical connectives.
(p ∧ q) → r
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You get an A on the final exam.q: You do every exercise in this book.r: You get an A in this class. Identify the expression for the proposition "You get an A on the final, you do every exercise in this book, and you get an A in this class" using p, q, and r and logical connectives (including negations).
p ∧ q ∧ r
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine whether the biconditional is true or false. 1 + 1 = 3 if and only if monkeys can fly.
true
The negation of the statement "121 is a perfect square" is "121 is not a perfect square."
true
Identify the negation of "Abby sent more than 100 text messages every day." (Check all that apply.)
Abby sent fewer than 100 text messages every day. There is a day that Abby sent at most 100 text messages.
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You have the flu.q: You miss the final examination.r: You pass the course. Identify the English translation of the compound proposition (p → ¬r) ∨ (q → ¬r).
If you have the flu then you will not pass the course, or if you miss the final exam then you will not pass the course. Correct
Identify an English translation that expresses the compound proposition p → q.
If you have the flu, then you miss the final examination.
Identify the negation of "Jennifer and Teja are friends."
Jennifer and Teja are not friends.
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. State the converse, contrapositive, and inverse of this conditional statement. Click and drag the named related conditionals to their corresponding statements of the conditional statement "I come to class whenever there is going to be a quiz."
The converse is "If I come to class, then there will be a quiz." The contrapositive is "If I don't come to class, then there won't be a quiz." The inverse is "If there is not going to be a quiz, then I don't come to class."
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. State the converse, contrapositive, and inverse of this conditional statement. Click and drag the named related conditionals to their corresponding statements of the conditional statement "A positive integer is a prime only if it has no divisors other than 1 and itself."
The inverse is "If a positive integer is not prime, then it has a divisor other than 1 and itself." The contrapositive is "If a positive integer has a divisor other than 1 and itself, then it is not prime." The converse is "A positive integer is a prime if it has no divisors other than 1 and itself."
(q → ¬p) ↔ (p ↔ q) pq ¬pq → ¬pp ↔ q(q → ¬p) ↔ (p ↔ q)TTFF CorrectTF CorrectTFFT CorrectFF CorrectFTTT CorrectFFFFTF IncorrectTT
The truth table for the compound proposition (q → ¬p) ↔ (p ↔ q) is pq ¬pq → ¬pp ↔ q(q → ¬p) ↔ (p ↔ q)TTFFTFTFFTFFFTTTFFFFTTTT
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Complete the truth table given below for the given proposition. p ↔ ¬p. p¬p p ↔ ¬pTF CorrectF CorrectFT CorrectF Correct
The truth table for the compound proposition p ↔ ¬p is p¬pp ↔ ¬pTFFFTF
p ⊕ (p ∨ q) . p q(p ∨ q)p ⊕ (p ∨ q)TTTT IncorrectTFTT IncorrectFTTF IncorrectFFFT Incorrect
The truth table for the compound proposition p ⊕ (p ∨ q) is p q(p ∨ q)p ⊕ (p ∨ q)TTTFTFTFFTTTFFFF
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Complete the truth table given below for the given proposition. p → ¬p. p¬pp → ¬pTFT IncorrectFTF Incorrect
The truth table for the proposition p → ¬p is p¬pp → ¬pTFFFTT
(p ↔ q) ⊕ (p ↔ ¬q) pq ¬qp ↔ qp ↔ ¬q(p ↔ q) ⊕ (p ↔ ¬q)TTFTFT CorrectTFTFTT CorrectFTFFTT CorrectFFTTFT Correct Explanation
The truth table of the compound proposition (p ↔ q) ⊕ (p ↔ ¬q) is pq ¬qp ↔ qp ↔ ¬q(p ↔ q) ⊕ (p ↔ ¬q)TTFTFTTFTFTTFTFFTTFFTTFT
(p ∧ q) → (p ∨ q). pqp ∧ qp ∨ q(p ∧ q) → (p ∨ q)TTTTTTFF CorrectT CorrectF IncorrectFTF CorrectF IncorrectT CorrectFFFFT
The truth table of the compound proposition (p ∧ q) → (p ∨ q) is pqp ∧ qp ∨ q(p ∧ q) → (p ∨ q)TTTTTTFFTTFTFTTFFFFT
Identify the negation of "There are 13 items in a baker's dozen." (Check all that apply.)
There are not 13 items in a baker's dozen. The number of items in a baker's dozen is not equal to 13.
Identify the negation of "There are 13 items in a baker's dozen." (Check all that apply.)
There are not 13 items in a baker's dozen.There are not 13 items in a baker's dozen. Correct There are 13 or less items in a baker's dozen.There are 13 or less items in a baker's dozen. Correct The number of items in a baker's dozen is not equal to 13.The number of items in a baker's dozen is not equal to 13. Correct The number of items in a baker's dozen is equal to 13.The number of items in a baker's dozen is equal to 13. Correct There are 13 or more items in a baker's dozen.
Identify the negation of "Abby sent more than 100 text messages every day." (Check all that apply.)
There is a day that Abby sent at least 100 text messages. Abby did not send more than 100 text messages every day.
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You have the flu.q: You miss the final examination.r: You pass the course. Identify the statement that express the compound proposition p ∨ q ∨ r as an English sentence.
You have the flu, or miss the final examination, or pass the course.
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. State the converse, contrapositive, and inverse of this conditional statement. Click and drag the named related conditionals to their corresponding statements of the conditional statement "If it snows today, I will ski tomorrow."
converse: If I am to ski tomorrow, it must snow today. If I am to ski tomorrow, it must snow today. Inverse: If it does not snow today, then I will not ski tomorrow. contrapositive: If I do not ski tomorrow, then it will not have snowed today.
Letp,q, andrbe the propositionsp: You have the flu.q: You miss the final examination.r: You pass the course. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. An English translation of the compound propositionq→ ¬ris "If you miss the final exam, then you pass the course."
false
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine whether the biconditional is true or false. 0 > 1 if and only if 2 > 1.
false
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine whether the biconditional is true or false. The truth value of the biconditional statement "1 + 1 = 2 if and only if 2 + 3 = 4" is true.
false
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You get an A on the final exam.q: You do every exercise in this book.r: You get an A in this class. Identify the expression for the proposition "You get an A on the final, but you don't do every exercise in this book; nevertheless, you get an A in this class" using p, q, and r and logical connectives (including negations).
p ∧ ¬q ∧ r
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You get an A on the final exam.q: You do every exercise in this book.r: You get an A in this class. Identify the expression for the proposition "To get an A in this class, it is necessary for you to get an A on the final" using p, q, and r and logical connectives (including negations).
r → p
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You get an A on the final exam.q: You do every exercise in this book.r: You get an A in this class. Identify the expression for the proposition "You will get an A in this class if and only if you either do every exercise in this book or you get an A on the final" using p, q, and r and logical connectives.
r ↔ (q ∨ p)
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You get an A on the final exam.q: You do every exercise in this book.r: You get an A in this class. Identify the expression for the proposition "You get an A in this class, but you do not do every exercise in this book" using p, q, and r and logical connectives (including negations).
r ∧ ¬q
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine whether the biconditional is true or false. 2 + 2 = 4 if and only if 1 + 1 = 2.
true
An English translation of the compound proposition ¬q ↔ r is "You do not miss the final exam if and only if you pass the course."
yes
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Let p, q, and r be the propositionsp: You have the flu.q: You miss the final examination.r: You pass the course. An English translation of the compound proposition (p ∧ q) ⊕ (¬q ∧ r) is "Either you have the flu and miss the final exam, or you do not miss the final exam and do pass the course."
yes
