CSE 260 Exam 1 Fall 2018
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CSE 260
Exam 1
Number of points = 40
Assume that universe of discourse is set of positive integers (1, 2, 3, …) unless specified otherwise
1. (3pts) Is the following a proposition (Yes or No)
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Yes |
No |
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5 + 7 = 10 |
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There are no black flies in Maine |
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Jennifer and Teja are friends (assume we are talking about two specific people) |
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3x (∀y x + y = 20) |
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121 is a perfect square |
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3x (4 + x = 5) |
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2. (7pts) Identify whether the following proposition is true
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True |
False |
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(1 + 1 = 2) ↔ (2 + 3 = 4) |
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(1 + 1 = 3) → (2 + 2 = 5) |
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Let P (x) be the proposition function x = x2 . 3x P(x) |
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3 n n2 < 0 |
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3 x (x2 = 2) [UoD = real numbers] |
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3 x (x + 1 > 2x) |
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0 > 1 ↔ 2 > 1 |
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3. (4pts) Show that the following statement is a tautology using truth table
(p ∧ q) → (p → q)
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p |
q |
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(p ∧ q) → (p → q) |
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F |
F |
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F |
T |
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T |
F |
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T |
T |
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(1 + 2) How many rows in the truth table of p → (q → r) result in the answer to be true.
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Answer = |
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Explain |
5. (5pts) Convert F(x, y) be the statement x can fool y where the universe of discourse is the set of all people in the world. Use quantifiers to express the following statements
a. Everybody can fool Fred
b. Everyone can be fooled by somebody
c. Nancy can fool exactly two people
d. Nancy can fool at least two people
e. None can fool himself/herself
6. (4pts) Show that the following is a tautology without using the truth table
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(p ∧ q) → (p → q) |
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7. (4 + 1pts) Prove the following
(3 k : n = 2k + 1) ∧ (3 k : m = 2k + 1) ⇒ (3 k : nm = 2k + 1)
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Justification |
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Write the meaning of above theorem in English. |
8. (2 + 4) Everyone who knows Java can get a high paying job. Everyone who has a high paying job plays golf. Someone in this class knows Java. Show that someone in this class plays golf.
Identify hypothesis and conclusion
Proof
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Justification |
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(1 + 2pts) Identify whether the following argument is correct or not
Every computer science major takes discrete mathematics
Natasha is taking discrete mathematics
Therefore, Natasha is a computer science major.
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The argument is ________________ (choose correct or incorrect) Explain your reason |
10.
11. A
12. A
13. Aa
2023-06-06