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Higher Nationals
Internal verification of assessment decisions – BTEC (RQF)
INTERNAL VERIFICATION – ASSESSMENT DECISIONS Programme title BTEC Higher National Diploma in Computing Assessor Internal Verifier Unit(s) Unit 18 : Discrete Mathematics Assignment title Discrete mathematics in software engineering concepts Student’s name S.M Nipuna Madhuranga Samarakoon List which assessment criteria the Assessor has awarded. Pass Merit Distinction INTERNAL VERIFIER CHECKLIST Do the assessment criteria awarded match those shown in the assignment brief? Y/N Is the Pass/Merit/Distinction grade awarded justified by the assessor’s comments on the student work? Y/N Has the work been assessed accurately? Y/N Is the feedback to the student: Give details:
- Constructive?
- Linked to relevant assessment criteria?
- Identifying opportunities for improved performance?
- Agreeing actions? Y/N Y/N Y/N Y/N Does the assessment decision need amending? Y/N Assessor signature Date Internal Verifier signature Date Programme Leader signature (if required) Date
Confirm action completed Remedial action taken Give details: Assessor signature Date Internal Verifier signature Date Programme Leader signature (if required) Date
Higher Nationals - Summative Assignment Feedback Form
Pearson Higher Nationals in Computing Unit 18: Discrete Mathematics
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Assignment Brief
Student Name /ID Number S.M Nipuna Madhuranga Samarakoon Unit Number and Title Unit 18: Discrete Mathematics Academic Year Unit Tutor Assignment Title Discrete mathematics in Computing Issue Date Submission Date IV Name & Date Submission Format: This assignment should be submitted at the end of the module, on the week stated at the front of this brief. The assignment can either be word-processed or completed in legible handwriting. If the tasks are completed over multiple pages, ensure that your name and student number are present on each page. Unit Learning Outcomes: LO1 Examine set theory and functions applicable to software engineering LO2 Analyze 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. Assignment Brief and Guidance:
Activity 01
Part 1
1. Let A and B be two non-empty finite sets. If cardinalities of the sets A, B, and A ∩ B^ are respectively 72, 28 and 13, then find the cardinality of the set A ∪ B^. 2. If n( A − B^ )=45, n( A ∪ B^ )=110 and n( A ∩ B^ )=15, then find n(B). 3. If n(A)=33, n(B)=36 and n(C)=28, find n( A ∪ B ∪ C^ ). Part 2 1. Write the multisets of prime factors for the given numbers. I. 160 II. 120 III. 250
- Write the multiplicities of each element of multisets in part 2(1-I, ii,iii) separately.
- Find the cardinalities of each multiset in part 2-1. Part 3
- Determine whether the following functions are invertible or not. If it is invertible, then find the rule
Part 3
- Check whether the following graphs have a Eulerian and/or Hamiltonian circuit. I. II.
III.
Part 4
- Construct a proof for the five color theorem for every planar graph.
- Discuss how efficiently Graph Theory can be used in a route planning project for a vacation trip from Colombo to Trincomalee by considering most of the practical situations (such as mileage of the vehicle, etc.) as much as you can. Essentially consider the two fold, - Routes with the shortest distance (Quick route travelling by own vehicle) - Route with the lowest cost
- Determine the minimum number of separate racks needed to store the chemicals given in the table (1st^ column) by considering their incompatibility using graph coloring technique. Clearly state you steps and graphs used. Chemical Incompatible with
- Consider the K-Maps given. For each K- Map i. Write the appropriate standard form (SOP/POS) of Boolean expression. ii. Draw the circuit using AND, NOT and OR gates. iii. Draw the circuit only by using i. NAND gates if the standard form obtained in part (i) is SOP. ii. NOR gates if the standard form obtained in pat (i) is POS. (a) AB/C 0 1 00 0 0 01 0 1 10 1 0 11 0 1 (b) AB/CD 00 01 10 11 00 1 0 0 1 01 0 1 0 1 10 1 1 1 1 11 1 1 0 1 (c) AB/C 0 1 00 1 0 01 1 1 10 0 1 11 1 0
Grading Rubric Grading Criteria Achieved Feedback 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 technique. D1 Formulate corresponding proof principles to prove properties about defined sets. LO2 Analyse mathematical structures of objects using graph theory. P3 Model contextualized 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 Eularian and Hamiltonian circuit exists in an undirected graph. D2 Construct a proof of the Five colour theorem. LO3 Investigate solutions to problem situations using the 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 Prepare a presentation that explains an application of group theory relevant to your course of study.
Activity 01 Part 1
1. Let A and B be two non-empty finite sets. If cardinalities of the sets A, B, and A ∩ B (^) are 72, 28 and 13 respectively, find the cardinality of the set A ∪ B (^).
n( A B ) = n(A) + n(B) - n( A B )
n( A B ) = 72 + 28 - 13
n( A B ) = 87
2. If n( A − B^ )=45, n( A ∪ B^ )=110 and n( A ∩ B^ )=15, then find n(B).
n( A B ) =
n( A B ) =
n( A B ) =
n( A B ) = n( A B ) + n( B A ) + n( A B )
110 = 45 + n( B A ) + 15 110 = 60 + n( B A ) n( B A ) = 50
n(B) = n( B A ) + n( A B )
n(B) = 50 + 15 n(B) = 65
P( A ∪ B^ ¿^ C^ )=?
P( A ∪ B^ ¿^ C^ )=P(A) + P(B)+ P(C) - P( A ∩ B^ ) - P( A ∩ C^ )-P( B ∩ C^ )
- Activity 01.................................................................................................
- Part 1....................................................................................................................................
- Part 2....................................................................................................................................
- Part 3....................................................................................................................................
- Part 4....................................................................................................................................
- Activity 02.................................................................................................
- Part 1....................................................................................................................................
- Part 2....................................................................................................................................
- 2...................................................................................................................................................
- Part 3...........................................................................................................................................
- Part 4....................................................................................................................................
- Activity 03.................................................................................................
- Part 1....................................................................................................................................
- Part 2....................................................................................................................................
- Part 3....................................................................................................................................
- Part 2....................................................................................................................................
- 1...................................................................................................................................................
- Part 4....................................................................................................................................
- Activity 04.................................................................................................
- Part 1....................................................................................................................................
- 2...................................................................................................................................................
- Part 2....................................................................................................................................
- 1...................................................................................................................................................
- 2...................................................................................................................................................
- Part 3....................................................................................................................................
- Part 4....................................................................................................................................
- P(A)=
- P(B)=
- P(C)=
- P(A)= 10+ a + 5+b =
- 15+a+b =
- a + b =
- 15+a+5+c =
- 20+ a+ c =
- a + c =
- 13+ 5+b+c =
- b + c= 28 –
- b + c =
- a + b =
- b + c=
- b + c =
- 1 +
- a + b – b-c =
- a - c =8
- 2 +
- 2a =
- a=
- b =
- c =
- P( A ∪ B ¿ C ) = 33+ 36+28- 17-11-
