MAT1101 Assignment 1 2020
S1 2020 MAT1101
Due date: Monday 10th May, XXXXXXXXXX:55pm AEST 1
MAT1101 ASSIGNMENT 2
SEMESTER 1, 2020
WEIGHT: 30% TOTAL MARKS 30
DUE DATE 10 May, 2020
ASSIGNMENT INSTRUCTIONS
• Show full working
easoning 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
easoning.
• 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: a
a and
aaabab. 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, XXXXXXXXXX:55pm AEST
2 marks i) Find ?(a
a) and ?(baaba).
2 marks ii) Find ?(10) and ?(22).
2 marks iii) Find (? ∘ ?)(a
a) and (? ∘ ?)(baaabab).
Question 2 [10 marks]
i) Consider the following circuit:
1 mark a) Write in mathematical notation, the logical expression
epresented 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, XXXXXXXXXX: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/