Download LO1. Examine set theory and functions applicable to software engineering LO2: Analyse math and more Schemes and Mind Maps Mathematics in PDF only on Docsity!
Higher Nationals
Assignment Brief – BTEC (RQF)
Higher National Diploma in Computing
Student Name /ID Number
Unit Number and Title
Unit 18 : Discrete Maths
Academic Year
Unit Assessor
Assignment Title
ASSIGNMENT 1- Set theory and functions- Graph theory
Issue Date
Submission Date
IV Name
Date
Submission Format:
This assignment should be submitted at the end of your lesson, on the week stated at the front of this brief.
The line spacing is 1.5, font is Times New Roman, and font size is 12. You are required to make use of
headings, paragraphs and subsections as appropriate, and all work must be supported with research and
referenced using the Harvard referencing system. Please also provide a bibliography using the Harvard
referencing system. Plagiarism will lead to the failure of the assignment. The recommended word limit is
3000 words, although you will not be penalised for exceeding the total word limit.
Unit Learning Outcomes:
LO1. Examine set theory and functions applicable to software engineering
LO2: Analyse mathematical structures of objects using graph theory
Assignment Brief and Guidance:
Part 1:
- Let A and B be two non-empty finite sets. If cardinalities of the sets A, B, and A ∩ B are 80 , 52
and 17 respectively, find the cardinality of the set A ∪ B.
- Let A={n∈N: 30 ≤n<50} and B={n∈N:10<n≤ 42 }. Suppose C is a set such that C⊆A and C⊆B.
What is the largest possible cardinality of C?
- Let A={1,2,…,10}. Define B 2
={B⊆A:|B|=2}. Find |B 2
- Consider the sets A and B, where A={3,|B|} and B={1,|A|,|B|}. What are the sets?
Part 2:
- Write the multi-sets of prime factors of given numbers.
a. 750
b. 3250
- Find the cardinalities of each multiset in part 2-1.
- Present the application of set and multiset in software engineering? Give specific programming
example
Part 3:
- Determine whether the following functions are invertible or not. If it is invertible, then find the rule
of the inverse f
(x)
a. f: 𝑅 → 𝑅
c. f: 𝑅
2
2
b. f: 𝑅
d. f:
[
]
[
]
1
𝑥
- Function f(x) =
5
9
(x-32) converts Fahrenheit temperatures into Celsius. What is the function for
opposite conversion?
- Present the application of function in software engineering? Give specific programming example
Part 4 :
- Formulate corresponding proof principles to prove the following properties about defined sets.
- De Morgan's Law by mathematical induction.
- Distributive Laws for three non-empty finite sets A, B, and C.
Part 5 :
- Discuss using two examples on binary trees both quantitatively and qualitatively.
Part 6 :
- State the Dijkstra's algorithm for a directed weighted graph with all non-negative edge weights.
- Find the shortest path spanning tree for the weighted directed graph with vertices A, B, C, D, and
E given using Dijkstra's algorithm.
Part 7 :
Check whether the following graphs have an Eulerian and/or Hamiltonian circuit.
Learning Outcomes and Assessment Criteria
Learning Outcome Pass Merit Distinction
LO1. Examine set
theory and functions
applicable to software
engineering
P1 Perform algebraic set
operations in a formulated
mathematical problem.
P2 Determine the
cardinality of a given
bag (multiset).
M1 Determine the inverse
of a function using
appropriate mathematical
techniques.
D1 Formulate
corresponding proof
principles to prove
properties about defined
sets.
LO 2 : Analyse
mathematical structures
of objects using graph
theory
P3 Model contextualised
problems using trees,
both quantitatively and
qualitatively.
P4 Use Dijkstra's
algorithm to find a
shortest path spanning
tree in a graph.
M2 Assess whether an
Eulerian and
Hamiltonian circuit
exists in an undirected
graph.
D2 Construct a proof of
the Five Colour
Theorem..
Higher Education Qualifications
Assignment Brief
