quiz2
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School
Technical Career Institutes *
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Course
288
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
9
Uploaded by jmortiz
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Started on
Wednesday, October 2, 2019, 7:13 PM
State
Finished
Completed on
Wednesday, October 2, 2019, 7:46 PM
Time taken
33 mins 40 secs
Grade
48.00
out of 100.00
Question 1
Correct
Mark 9.00 out of 9.00
Question text
Write a wff for the following expression:
A is derived from B
Answer: Feedback
The correct answer is: B --> A
Comments
Comment: Question 2
Correct
Mark 6.00 out of 6.00
Question text
Is the following wff a Tautology, Contradiction or neither?
(A→B) ↔ A' V B
B->A
Answer: Feedback
The correct answer is: Tautology
Question 3
Complete
Mark 1.00 out of 9.00
Question text
| 0 0 1| |0 1 1|
A= |1 1 0| B= |0 0 0|
|1 0 0| |1 0 0|
Find A V B:
1 0 0
0 1 1
0 1 1
Feedback
Comments
Comment: Question 4
Partially correct
Mark 1.00 out of 9.00
tautology
Question text
Write a wff for the following expression:
A
exactly when B
Answer: Feedback
Correct answer
The correct answer is: A <--> B
Comments
Comment: Question 5
Correct
Mark 6.00 out of 6.00
Question text
[(A V B) Λ C'] →A' V C
Select one:
a. Neither b. Tautology c. Contradiction Feedback
Your answer is correct.
The correct answer is: Neither
A=B
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Question 6
Correct
Mark 10.00 out of 10.00
Question text
22 members of an athletic club are surveyed by the owners. Of these, 10 are surfers, 16
are runners, and 13 are bikers. 7 of the surfers are also runners, and 6 of the surfers are also bikers. 9 people are both bikers and runners. How many people participate in all three sports?
Answer: Feedback
A = set of surfers
B = set of runners
C = set of bikers
|A U B U C| = 22
|A| = 10
|B| = 16
|C| = 13
|A ∩ B| = 7
|A ∩ C| = 6
|B ∩ C| = 9
Principle of Inclusion and Exclusion for three sets:
|A U B U C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C |
22 = 10 + 16 + 13 - 7 - 6 - 9 + |A ∩ B ∩ C |
|A ∩ B ∩ C | = 5
The correct answer is: 5
Question 7
Partially correct
Mark 1.00 out of 12.00
Question text
5
License plates in a certain state are either "regular" plates, which have 2 letters followed by 3 digits, or
"vanity" plates, which have 5 letters. For either category, the plate can be either plain (blue letters on a white background) or a special environmental
plate (green letters on a white background with a picture of the state bird, the buzzard).
How many different plates can be issued? Answer: Feedback
The correct answer is: (26.26.10.10.10.2) + (26.26.26.26.26.2) = 25,114,752.
Comments
Comment: Question 8
Correct
Mark 1.00 out of 1.00
Question text
How many people must be in a room to guarantee that two people have a last name that begins with the same initial?
Answer: Feedback
26 letters in the alphabet.
27 people will ensure have at least one duplicate.
The correct answer is: 27
Question 9
Correct
Mark 10.00 out of 10.00
24748360
27
Question text
Let:
A:
roses are red.
B:
violets are blue.
C:
sugar is sweet.
Translate the following compound statements into symbolic notation.
Roses are red and, if sugar is sour, then either violets aren't blue or sugar is sweet.
Answer: Feedback
The correct answer is: A Λ [C' → ( B' V C)]
Comments
Comment: Question 10
Incorrect
Mark 0.00 out of 6.00
Question text
(A →B) →[(A V C) →(B V C)]
Select one:
a. Contradiction b. Neither c. Tautology Feedback
Your answer is incorrect.
The correct answer is: Tautology
A^`C->`BVC
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Question 11
Complete
Mark 0.00 out of 10.00
Question text
Given the matrices:
|4 3 -2| |2 -1|
A= |1 3 5| B= |4 3|
|0 3|
Find A • B
8 12 0
-4 9 -6
2 12 0
-1 9 15
Feedback
|20 -1|
A • B = |14 23|
Comments
Comment: Question 12
Incorrect
Mark 0.00 out of 3.00
Question text
The following wff is a Tautology:
(A V B)' ↔ A' Λ B'
Select one:
True False Feedback
The correct answer is 'True'.
Question 13
Partially correct
Mark 3.00 out of 9.00
Question text
Using the letters indicated for the component statement, translate the following compound s
tatement into symbolic notation.
A:
it will rain;
B:
it will snow
Either it will rain or it will snow but not both.
Answer: Feedback
The correct answer is: (A V B) Λ (A Λ B)'
Comments
Comment: (AVB)'
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