[Solved] COMP9020 Week 1-Numbers, Sets, Words, Logic

Numbers, Sets, Words, Logic

1. (Numbers)

How many numbers in the interval [1431,9758] are

1. divisible by 3?
2. divisible by 5?
3. divisible by 3 and 5?
4. divisible by 3 or 5?

2. (Sets)

Prove that

1. using Venn diagrams,
2. without Venn diagrams.

4. (Propositional Logic)

For each of the following formulae, determine all the truth assignments to , and under which

5. (Proving properties of algorithms)

Recall the algorithm for computing the greatest common divisor (gcd) of two positive numbers:

1 of 2 17/02/2020, 4:18 pm COMP9020 20T1 Week 1 Problem Set https://cgi.cse.unsw.edu.au/~cs9020/20T1/probs/prob1/index.php

Recall the correctness proof given in class. What needs to be changed to adapt it to the faster version below?

6. Challenge Exercise

A multiplication magic square has the product of the numbers in each row, column and diagonal the same. If the diagram below is filled with positive integers to form a multiplicative magic square, then give the value of y.