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BTEC Higher National Diploma in Computing
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Unit(s)
Unit 18 : Discrete Mathematics
Assignment title
Discrete mathematics in software engineering concepts
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Pearson
Higher Nationals in
Computing
Unit 18 : Discrete Mathematics
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Assignment Brief
Student Name /ID Number
Unit Number and Title Unit 18 :Discrete Mathematics
Academic Year 2021/
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Assignment Title Discrete mathematics in Computing
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on each sheet of paper.
Unit Learning Outcomes:
LO1 Examine set theory and functions applicable to software engineering.
LO2 Analyse mathematical structures of objects using graph theory.
LO3 Investigate solutions to problem situations using the application of Boolean algebra.
LO4 Explore applicable concepts within abstract algebra.
ii. De Morganās Law by mathematical induction.
iii. Distributive Laws for three non-empty finite sets A, B, and C.
Activity 02
Part 1
- Model two contextualized problems using binary trees both quantitatively and qualitatively.
Part 2
- State the Dijkstraās algorithm for a directed weighted graph with all non-negative edge
weights.
- Use Dijkstraās algorithm to find the shortest path spanning tree for the following weighted
directed graph with vertices A, B, C, D, and E given. Consider the starting vertex as E.
Part 3
- Assess whether the following undirected graphs have an Eulerian and/or a Hamiltonian cycle.
i.
ii.
iii.
Part 4
- Construct a proof of the five color theorem for every planar graph.
(b)
AB/CD 00 01 11 10
(c)
AB/C 0 1
Activity 04
Part 1
- Describe the distinguishing characteristics of different binary operations that are performed on the
same set.
Part 2
- Determine the operation tables for group G with orders 1, 2, 3 and 4 using the elements a, b, c, and
e as the identity element in an appropriate way.
i. State the relation between the order of a group and the number of binary operations that can
be defined on that set.
ii. How many binary operations can be defined on a set with 4 elements?
i. State the Lagrangeās theorem of group theory.
ii. For a subgroup H of a group G, prove the Lagrangeās theorem.
iii. Discuss whether a group H with order 6 can be a subgroup of a group with order 13 or not.
Clearly state the reasons.
Part 3
- Validate whether the set
S =āā{ā 1 }
is a group under the binary operation ā*ādefined as
a ā b = a + b + ab
for any two elements
a , b ā S
Part 4
- Prepare a presentation for ten minutes to explore an application of group theory relevant to
your course of study. (i.e. in Computer Sciences)
application of Boolean algebra.
P5 Diagram a binary problem in the application of Boolean Algebra.
P6 Produce a truth table and its corresponding Boolean equation from
an applicable scenario.
M3 Simplify a Boolean equation using algebraic methods.
D3 Design a complex system using logic gates.
LO4 : Explore applicable concepts within abstract algebra.
P7 Describe the distinguishing characteristics of different binary
operations that are performed on the same set.
P8 Determine the order of a group and the order of a subgroup in
given examples.
M4 Validate whether a given set with a binary operation is indeed a
group.
D4 Explore with the aide of a prepared presentation the application of
group theory relevant to your course of study
