Kingdom of Saudi Arabia
Ministry of Higher Education
JEDDAH UNIVERSITY
Computing and Information technology
Faculty (Al Kamil)
‫جامعة جدة‬
Name
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Exam:
Semester :
CICS 220/ITCP 213
Discrete Structure
Thu. 3-03-2016
9.00 – 10.30
First Exam
1st Semester1436/1437 AH
Marks
25
Part One
10 Marks
This is a multiple choice question, Insert X under the right answer in the cover sheet.
1. Convert into connectives "To take discrete mathematics, you must have taken calculus
or a course in computer science"
A) Q V R P
B) P  Q V R
C) P  Q  R
D) Q  R P
2. The proposition  p => q is called the ___________________ of p=>q
A) Converse
B) Contrapositive
C) Inverse
D) Contradiction
3. Which type of equivalence law P(QR)  (PQ)  (PR)
A) Associative laws
B) De Morgan’s laws
C) Domination laws
D) Distributive laws
4. Which type of rule of inference (q ∧ (p ⇒ q)) ⇒ p
A) Modus ponens
C) Hypothetical syllogism
B) Modus tollens
D) Addition
5. If O= {x | x is an even positive integer less than 12} then O=__________?
A) O= {1,3,5,7,9,11}
B) O= {1,2,4,6,8,10}
C) O= {1,2,3,4,5,6,7,8,9,10,11}
D) O= {2,4,6,8,10}
6. If A = {x, y, z} the power set of A is P (A) =
A) P(A) = {{x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}
B) P(A) = {,{x}, {y}, {z}, {x, y}, {x, z}, {y, z}}
C) P(A) = {, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}},{x, y, z}}
D) None
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7. Equivalence for  (p  q) ≡
A) (p ∧ q)
C) (p ∧ q)
B) (p V q)
D) (p V q)
8. What does xy (x + y = 320) mean ?
A) “There exists a x for every y so that x + y = 320.”
B) “For every x there exists a y so that x + y = 320.”
C) Both
D) None of the above
9. Modus Ponen is also known as __________
A) Affirming the Consequent or
C) Denying the Antecedent
B) Law of Detachment
D) None of them
10. Cardinality of |AUB| =
A) |AUB| = |A|. |B|
C) |AUB| = |A| +|B|- |AB|
B) |AUB| = |A| + |B|
D) |AUB| = |A| +|AB|
Part Two
Answer the following questions
10 Marks
1. a) Express the Negation of the statement
x y (xy=1)
_______________________________________________________________
_______________________________________________________________
b) Translate the statement "The sum of two positive integers is always positive" into a
a logical expression
_______________________________________________________________
_______________________________________________________________
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2. Find the Truth table for (PQ) (P)  (Q).
3.
(P(PQ))
= (PQ) can be simplified by using the following series of logical
equivalence
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4. Write Converse, Contrapositive & Inverse for the following Sentence?
“If it is raining, then I get wet”
5. What is the Cartesian Product AxBxC where A={0,1}, B={1,2}, C={2,3,4}
Solution:
Part Three
Find the true or false
5 Marks
1. A statement that can be either true or false, depending on the truth values of its
propositional variables, is called an Absurdity.
[
2. If p=>q is an implication, then its converse is the implication q => p [
3. “y > 5” is a Proposition
[
4. Predicate contains a variable e.g.: x-3 > 5
[
]
]
]
]
5. A= {1, 2, 3}, B= {2, 3, 4}, A ⊆ B?
]
[
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