[SOLVED] COMP9020-Set 1 Numbers, Sets, Words and Logic

Description

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 number

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.