plz find question file.
MAT1101 Assignment 1 2020 S1 2020 MAT1101 Due date: Monday 10th May, 2020 11:55pm AEST 1 MAT1101 ASSIGNMENT 2 SEMESTER 1, 2020 WEIGHT: 30% TOTAL MARKS 30 DUE DATE 10 May, 2020 ASSIGNMENT INSTRUCTIONS • Show full working/reasoning for each question. Give the marker every opportunity to see how you obtained your answers. Your reasoning is just as important as the final answer. Part marks for each question will be awarded based on your reasoning. • Clear communication and good presentation will make it easier for the marker to give you marks for each question. Tips on mathematical communication, see the USQ Learning and Teaching Support “Maths QuickTips” and Appendix B: Technical Communication of the Study Book. • Generally, in all your calculations, use as many decimal places as your calculator will allow. Only round your final answers. ASSIGNMENT QUESTIONS Question 1 [10 marks] i) ? and ? are defined as follow: ?(?) = ?3 and?(?) = ? − 1 ∀? ∈ ℝ 2 marks i) Find (? ∘ ?)(2) and (? ∘ ?)(2). 2 marks ii) Find (? ∘ ?)(?) and (? ∘ ?)(?). ii) Let ? be the set of all possible strings containing only ? and ?’s. For example: two elements of ? are the strings: abba and baaabab. Let ? ∶ ? → ℤ be the length function, such that: ?(?) = the total number of characters in ?, ∀? ∈ ?. For example: ?(???) = 3. Let ? ∶ ℤ → {0, 1, 2, 3, 4, 5, 6, 7} ∶ ?(?) = ? mod 8, ∀? ∈ ℤ. For example: ?(5) = 5 mod 8 = 5. https://lor.usq.edu.au/usq/file/f391ad40-fd5e-4c3d-a1d2-add2ef63c6fc/1/OER_maths_comm.pdf MAT1101 S1 2020 2 Due date: Monday 10th May, 2020 11:55pm AEST 2 marks i) Find ?(abba) and ?(baaba). 2 marks ii) Find ?(10) and ?(22). 2 marks iii) Find (? ∘ ?)(abba) and (? ∘ ?)(baaabab). Question 2 [10 marks] i) Consider the following circuit: 1 mark a) Write in mathematical notation, the logical expression represented by this circuit. 2 marks b) Construct the truth table for the above circuit. 2 marks c) Construct a Karnaugh Map for the circuit. 2 marks d) Hence, or otherwise show that the circuit is equivalent to: ? ∨ ¬? . 3 marks ii) Prove the following statement using mathematical induction. 1. S1 2020 MAT1101 Due date: Monday 10th May, 2020 11:55pm AEST 3 Question 3 [10 marks] i) The Symmetric Difference of sets ? and ? is denoted by ? ⊕ ?. ? ⊕ ? is the set containing the elements in either ? or ?, but not in both ? and ?. 2 marks i) Find the symmetric difference of {1, 3, 5} and {1, 2, 3} 2 marks ii) Illustrate on a Venn diagram the symmetric difference of the sets ? and ?. iii) Using Venn Diagrams show that the following laws are true for the symmetric difference. 2 marks i. ? ⊕ ? = (? ∪ ?) − (? ∩ ?) 2 marks ii. ? ⊕ ? = (? − ?) ∪ (? − ?) 2 marks ii) Using Venn diagrams find the sets ? and ? if ? − ? = {1, 5, 7, 8}, ? − ? = {2, 10} and ? ∩ ? = {3, 6, 9}. END OF ASSIGNMENT QUESTIONS Scanning hand written assignments Some recommendations for scanning a hand written assignment. • Use a black pen; as it will scan better. • Scan at 150 – 200 dpi. • Depending on your scanner you may need to either combine your images into a single document using Word, Preview (Mac OS X) or the free PDF Toolkit. https://www.pdflabs.com/tools/pdftk-the-pdf-toolkit/