Winter 2017: Solved Questions 1
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
[Basic Mathematics]
1. What is Log4(1024)? Show how you determine the result.
Ans:
=
Log4(1024) = ( ) = () = 5
2. Given () = solve f
Key Concepts in Computer Science (60-100)
Basic Structures: Sets
Set Operations
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Set Operations
2
Key Concepts in Computer
Key Concepts in Computer Science (60-100)
Review of Basic Mathematical Concepts
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Review of Basic Mathematical Concepts - Ou
Key Concepts in Computer Science (60-100)
Pseudocode
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Algorithm
An algorithm is a sequence of unambiguous instructions for
Key Concepts in Computer Science (60-100)
Basic Structures: Functions
Functions
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Functions
2
Key Concepts in Computer Scien
Winter 2017: Lab 2
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, January 19, 2017.
Hand in: handwritten or word processor.
1. [4 marks] Construct a truth table for: (r q) (p r).
Key Concepts in Computer Science (60-100)
Induction and Recursion
Recursive Algorithms
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Recursive Algorithms
2
Key Concepts
Key Concepts in Computer Science (60-100)
The Foundations: Logic and Proofs
Propositional Satisfiability, Predicates and Quantifiers
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Comput
Key Concepts in Computer Science (60-100)
The Foundations: Logic and Proofs
Applications of Propositional Logic
Propositional Equivalences
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in
Winter 2017: Solved Questions 5
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
[Proof Methods and Strategies]
1. Use a proof by cases to show that min(a, min(b, c) = min(min(a, b), c) whenever a, b, and c are
inte
Winter 2017: Lab 5
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, February 9, 2017.
Hand in: handwritten or word processor.
[Proof Methods and Strategies]
1) [5 marks] Use a proo
Winter 2017: Lab 11 (Optional)
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Held: In your lab section Thursday, March 30, 2017.
Hand in: nothing (Review Lab).
Winter 2017: PRACTICE FINAL EXAM
[Logic]
1. Write th
Winter 2017: Solved Questions 10
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
[Mathematical Induction]
1. Prove using the Principle of Mathematical Induction that 3 + (35) + (352) + + (35n) =
(3(5n+1 - 1)/4 when
Key Concepts in Computer Science (60-100)
The Foundations: Logic and Proofs
Propositional Logic
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Propositional Logic
2
Key
Winter 2017: Lab 9
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, March 16, 2017.
Hand in: handwritten or word processor.
Write your answers clearly. If we cannot read it, we can
Winter 2017: Solved Questions 8
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
[Functions]
1) Determine whether each of these functions from Z to Z is one-to-one.
a) f(n) = n 1
Ans: This is one to one. Any y codom
Key Concepts in Computer Science (60-100)
Introduction
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Why do many students perform below
their potential in Computer Scie
Winter 2017: Lab 4
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, February 2, 2017.
Hand in: handwritten or word processor.
1. [2 marks] What is the rule of inference used in the
Winter 2017: Solved Questions 9
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
[Algorithms]
1) List all the steps used to search for 9 in the sequence 1, 3, 4, 5, 6, 8, 9, 11 using
a) a linear search.
Ans:
we chec
Key Concepts in Computer Science (60-100)
The Foundations: Logic and Proofs
Nested Quantifiers
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Nested Quantifiers
2
Key Co
Winter 2017: Lab 3
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, January 26, 2017.
Hand in: handwritten or word processor.
1. [2 marks] Let P(x) denote the statement that x2 > 4
Winter 2017: Solved Questions 7
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
[Basic Mathematics]
1. Simplify these expressions using the rules for logarithms. Your answer will be a simpler formula. You do
not ne
Winter 2017: Lab 1
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, January 12, 2017.
Hand in: handwritten or word processor.
Do not use a calculator.
1. [1 mark] What is Log4(4096
Key Concepts in Computer Science (60-100)
The Foundations: Logic and Proofs
Rules of Inference
School of Computer Science
Faculty of Science
University of Windsor
Dr. Scott Goodwin
Winter 2017
1
Key Concepts in Computer Science
Rules of Inference
2
Key Co
Winter 2017: Solved Questions 3
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
[Predicates]
1. Suppose that the domain of the propositional function P(x) is cfw_4, -3, 1, -5. Express these statements
without using
60-100 Formula Sheet Winter 2017
Key Concepts in Computer Science
School of Computer Science
For b>0 and b1
Basic Mathematics
|a| = a if a 0, -a if a < 0
an = a a aa (n factors)
Logb(n) = p
|ab| = |a|b|
a0 = 1 (for a 0)
Logb(xn) = nLogb(x)
|a/b| = |a|/|b|
Winter 2017: Lab 10
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, March 23, 2017.
Hand in: handwritten or word processor.
Write your answers clearly. If we cannot read it, we ca
Winter 2017: PRACTICE MIDTERM B
(with solutions)
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
NOTES:
The time limit is 120 minutes. The exam is out of 120 marks.
Answer all questions in the test booklet.
Put you
Winter 2017: Lab 8
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, March 9, 2017.
Hand in: handwritten or word processor.
[Functions]
1. [4 marks] Determine whether each rule belo
Winter 2017: Lab 6
60-100 Key Concepts in Computer Science
School of Computer Science
University of Windsor
Due: In your lab section Thursday, February 16, 2017.
Hand in: handwritten or word processor.
[Set Operations]
1. [5 marks] Prove the absorption la