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MAT1101 Discrete Mathematics for Computing Assignment 2 Total marks: 30 Weighting: This cover sheet is available online via UConnect. Print your...

Discrete Maths problems.

- 1 - MAT1101 Discrete Mathematics for Computing Assignment 2 Total marks: 30 Weighting: 20% Due 5pm Friday 18 May 2012 Instructions Submit this assignment on paper, not electronically. Attach an assignment cover sheet to the front of your assignment. This cover sheet is available online via UConnect. Print your cover sheet and sign it. On campus students submit their assignments at the Faculty of Science Reception W- Block 5 th Floor External students mail their assignment to Distance and e-Learning Centre University of Southern Queensland TOOWOOMBA QLD 4350 AUSTRALIA Hand-written assignments are perfectly acceptable. You may choose to typeset your assignment if you wish but you must ensure that all mathematical notations and symbols follow standard mathematical conventions. Show full working for all questions. Give the marker every opportunity to see how you obtained your answers.
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- 2 - Question 1 [6 marks] (a) Draw a truth table to show that the two expressions [ ( )] p p q q  and () pq  are logically equivalent. Use classical truth table notation with T for True and F for False. [2 marks] (b) Use the laws of logic to show that the expression [( ) ( )] ( ) p q r p r p       is a tautology. Be sure to name each law you use at each step. [4 marks] Question 2 [4 marks] Consider the set { 1, 0, 1} A  . (a) Write down its power set P ( A ). [1 mark] (b) The relation ‘is a subset of’ defined on this power set P ( A ) is a partial order relation. In other words, this relation is reflexive, anti-symmetric and transitive. Express each of these three properties in concise form using all the mathematical symbols and notation learned in this course. Use the letters X , Y and Z to denote any of the elements of this power set. [3 marks] Question 3 [6 marks] The function t ( n ) is defined recursively as follows 0, 1 ( ) 1, 2 ( 2) 2 ( 1) 1, 3 n t n n t n t n n n      (a) Write, in pseudocode, an iterative algorithm for this function. Your function must take as input the single number n and return as output the vector [ (1), (2), , ( )] t t t t n . Be sure to declare your function with an appropriate name. [4 marks] (b) Trace your algorithm for the input n = 5. [2 marks]
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