## Description

Objectives: Proof Techniques (I) Instruction

This is a written assignment and is worth 30% of the marks for individual assignments. Please type your answers or write in legible handwriting. Answers that are messy and hard to read will be deducted marks.

Part A) Problems and Proofs (6 points)

Rewrite the following claim as a universal proposition in symbolic form:

โThe algorithm bruteForceSearch() is a linear-time algorithmโ.

and use the strategy of generalizing from generic particular to prove that the claim is correct. For a detailed explanation of the claim and related concepts in algorithm analysis, see the figure on the next page.

Part B) Proof by Cases (6 points)

Use the method of proof by cases to prove the following statement

โn โฅ 3, n2 โ 3n + 3 is odd.

Part C) Do Question 4.52 in the textbook (Section 4.3) (6 points)

Part D) Do Question 4.56 in the textbook (Section 4.3) (6 points)

Part E) (Proof by Induction) Do Question 5.1 in the textbook (Section 5.2) (6 points)

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Individual Assignment 02: COSC 221 (UBCO)

More Information on Part A.

The claim is about the running time of an algorithm described as a Java method in Figure 1.

The running time of an algorithm is measured by the number of โprimitive stepsโ required to complete the execution of the algorithm. For our purpose, letโs count each program statement in the Java code as one primitive step. An algorithm is said to be a linear-time algorithm if its running time for any input is no greater than the number of elements in the input multiplied by some constant (a value that doesnโt depend on the number of elements in the input).

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