quiz%20u6%20discrete%20math.pdf

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A linear homogeneous recurrence relation with constant coefficients can always be solved using the characteristic equation. Question 1 Select one: True False Feedback The correct answer is 'True'. Question 2 Incorrect Mark 0.00 out of 1.00 Flag question Question text
Let ‘a n ’ be a sequence defined as a n = 4, 7, 11, 16…. What will be the value of a 2024 – a 2023 with the initial condition a 1 = 4? Question 2 Answer a. 2022 b. 2025 c. 2023 d. 2026 Feedback Your answer is incorrect.
The correct answer is: 2025 Question 3 Correct Mark 1.00 out of 1.00 Flag question Question text A relation R = ‘ ’ from A= {Bernadine, Azeez, Russel, Frank} to B = {Bennett, Ahmed, Ria, Feroza}is represented as: Which of the following relations suits best for the given representation?
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Question 3 Answer a. Such that x y iff x and y share the first letter. b. Such that x y iff x and y share gender status. c. Such that x y iff x and y share the same country. d. Such that x y iff x and y are friends. Feedback Your answer is correct. The correct answer is:
Such that x y iff x and y share the first letter. Question 4 Incorrect Mark 0.00 out of 1.00 Flag question Question text Which of the following statements is the contrapositive of the statement, “I will see a doctor if the pain doesn’t go away.” Question 4 Answer a. If I do not see a doctor, my pain goes away. b.
If my pain goes away, I will not see a doctor. c. If my pain goes away, I will see a doctor. d. If I see a doctor, my pain goes away. Feedback Your answer is incorrect. The correct answer is: If I do not see a doctor, my pain goes away. Question 5 Correct Mark 1.00 out of 1.00 Flag question
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Question text Which rule of inference is used for the following? ‘Ruth will join as an intern at TCS this summer. Therefore, this summer Ruth will join TCS as an intern or she will go on a trip.’ Question 5 Answer a. Simplification b. Conjunction c. Addition d. Disjunctive syllogism
Feedback Your answer is correct. The correct answer is: Addition Question 6 Incorrect Mark 0.00 out of 1.00 Flag question Question text An engineer is constructing a building. It is known that it will take 20% more time to build each subsequent floor of the building. If it takes 4 months to build the ground floor of the building, how long will it take to complete the construction of a 6-floor building? (Select the most appropriate option).
Question 6 Answer a. 8 months b. One year c. 1 year 4 months d. 1 year 2 months Feedback Your answer is incorrect. The correct answer is: One year
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Question 7 Correct Mark 1.00 out of 1.00 Flag question Question text Let R be a relation defined by using Boolean arithmetic, then: Question 7 Answer a. b.
c. d. Feedback Your answer is correct. The correct answer is: Question 8
Correct Mark 1.00 out of 1.00 Flag question Question text Identify the diagram. Question 8 Answer a. The Hasse Diagram of a POSET. b. The Hasse diagram is not a Partial order.
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c. The Hasse Diagram is an equivalence relation. d. The Hasse Diagram is reflexive. Feedback Your answer is correct. The correct answer is: The Hasse Diagram of a POSET. Question 9 Correct Mark 1.00 out of 1.00 Flag question Question text
In a hypothetical chemical reaction, the number of molecules of products increases by a factor of k every second. Initially, there were two molecules of products present. After 7 seconds, there were 4374 molecules present. What is the value of k? Question 9 Answer a. 3 b. 2 c. 4 d. 1 Feedback Your answer is correct.
The correct answer is: 3 Question 10 Correct Mark 1.00 out of 1.00 Flag question Question text A function is defined as F (n) = 5F (n - 1) -6F (n-2), F (0) = 3, F (1) = 7. If the degree of the above recurrence relation is 2, solve the above recurrence relation using the characteristic root method. Question 10 Answer
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a. F(n) = 3 n + 2 n+1 b. F(n) = 3 n+1 + 2 n c. F(n) = 3 n + 2 n-1 + 2 d. F(n) = 3 n + 2 n Feedback Your answer is correct. The correct answer is: F(n) = 3 n + 2 n+1 Question 11 Incorrect
Mark 0.00 out of 1.00 Flag question Question text The statement p q is equivalent to ¬(p ∧ q). Question 11 Select one: True False Feedback The correct answer is 'False'. Question 12 Correct Mark 1.00 out of 1.00
Flag question Question text The statement ‘Every clown is glowing’, where c(x): x is clown and f(x): x is glowing, and the domain consisting of all clowns can be written as ________. Question 12 Answer a. ∃ x(C(x) ∨ F(x)) b. ∀ x(C(x) ∧ F(x)) c. ∃ x(C(x)↔F(x)) d. ∀ x(C(x)→F(x))
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Feedback Your answer is correct. The correct answer is: ∀ x(C(x)→F(x)) Question 13 Correct Mark 1.00 out of 1.00 Flag question Question text Solve the following recurrence relation using the iterative method. 2a n = 6a n-1 – 4 (a 0 = 1) Question 13
Answer a. a n = 1 b. a n = 3 n - 2 c. a n = 2.3 n -4 d. a n = 2 n - 3 Feedback Your answer is correct. The correct answer is: a n = 1 Question 14
Correct Mark 1.00 out of 1.00 Flag question Question text Which of the following statements is NOT equivalent to the statement, “There exists either a historian or a philosopher who knows the work of both Galileo and Dante.” Question 14 Answer a. There exists a person who is a Historian and who knows the work of both Galileo and Dante or there exists a person who is a philosopher and who knows the work of both Galileo and Dante. b.
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There exists a person who is a Historian or there exists a person who is a philosopher who knows the work of Galileo or who knows the work of Dante. c. There exists a Historian and who knows the work of both Galileo and Dante or there exists a philosopher who knows the work of both Galileo and Dante. d. There exists a Historian who knows the work of both Galileo and Dante or there exists a person who is a philosopher who knows the work of both Galileo and Dante. Feedback Your answer is correct. The correct answer is: There exists a person who is a Historian or there exists a person who is a philosopher who knows the work of Galileo or who knows the work of Dante. Question 15
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Correct Mark 1.00 out of 1.00 Flag question Question text A fixed amount is kept on a compound interest rate of r percent per year, if P 0 is the initial amount, generate the recurrence relation for the principal amount after n years, P n (inclusive of interest). Question 15 Answer a. P n = rP n-1 b. P n = (1 + r)P n-1 c.
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P n = (1 - r)P n-1 d. P n = (r - 1)P n-1 Feedback Your answer is correct. The correct answer is: P n = (1 + r)P n-1
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