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Discrete Mathematics
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,DILAKSON
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 1
Discrete Mathematics Assessor signature Date Internal Verifier signature Date Programme Leader signature (if required) (^) Date 2
Higher Nationals - Summative Assignment Feedback Form
Student Name/ID S,DILAKSON 15077 Unit Title Unit 18 : Discrete Mathematics Assignment Number^1 Assessor Submission Date Date Received 1st submission Re-submission Date Date Received 2nd submission Assessor Feedback: LO1 Examine set theory and functions applicable to software engineering. Pass, Merit & Distinction Descripts
P1 P2 M1 D
LO2 Analyse mathematical structures of objects using graph theory. Pass, Merit & Distinction Descripts
P3 P4 M2 D
LO3 Investigate solutions to problem situations using the application of Boolean algebra.
Pass, Merit & Distinction Descripts
P5 P6 M3 D
LO4 Explore applicable concepts within abstract algebra.
Pass, Merit & Distinction Descripts
P7 P8 M4 D
Grade: Assessor Signature: Date: Resubmission Feedback: Grade: Assessor Signature: Date: Internal Verifier’s Comments: Signature & Date:
- Please note that grade decisions are provisional. They are only confirmed once internal and external moderation has taken place and grades decisions have been agreed at the assessment board. 4
Pearson Higher Nationals in Computing Unit 18: Discrete Mathematics 5
- If you are proven to be guilty of plagiarism or any academic misconduct, your grade could be reduced to A REFERRAL or at worst you could be expelled from the course 7
Student Declaration I hereby, declare that I know what plagiarism entails, namely to use another’s work and to present it as my own without attributing the sources in the correct way. I further understand what it means to copy another’s work.
- I know that plagiarism is a punishable offence because it constitutes theft.
- I understand the plagiarism and copying policy of the Edexcel UK.
- I know what the consequences will be if I plagiaries or copy another’s work in any of the assignments for this program.
- I declare therefore that all work presented by me for every aspect of my program, will be my own, and where I have made use of another’s work, I will attribute the source in the correct way.
- I acknowledge that the attachment of this document signed or not, constitutes a binding agreement between myself and Edexcel UK.
- I understand that my assignment will not be considered as submitted if this document is not attached to the attached. [email protected] Student’s Signature Date: ( Provide E-mail ID ) ( Provide Submission Date ) 8
Contents
Activity 01
Part 01
1. A ∪ B^?
2. n ( B )?
3. n ( A ∪ B ∪ C )=?
n ( A )= 33
n ( B )= 36
n ( C ) = 28
Figure 1 Venn diagram
n ( A ∪ B ∪ C )= n ( A ) + n ( B ) + n ( C )− n ( A ∩B )− n ( A ∩C )− n ( B∩ C )
- Activity 01..............................................................................................................................................
- Part 01...............................................................................................................................................
- Part 02...............................................................................................................................................
- Part 03...............................................................................................................................................
- Part 04.............................................................................................................................................
- Activity 02............................................................................................................................................
- Part 01.............................................................................................................................................
- Part 02.............................................................................................................................................
- Part 03.............................................................................................................................................
- Part 04.............................................................................................................................................
- Activity 03............................................................................................................................................
- Part 01.............................................................................................................................................
- Part 02.............................................................................................................................................
- Part 03.............................................................................................................................................
- Part 04.............................................................................................................................................
- Activity 04............................................................................................................................................
- Part 01.............................................................................................................................................
- Part 02.............................................................................................................................................
- Part 03.............................................................................................................................................
- References...........................................................................................................................................
- Figure 1 Venn diagram...........................................................................................................................
- Figure 2De Morgan's Law....................................................................................................................
- Figure 3 Binary Tree.............................................................................................................................
- Figure 4 Full Binary tree.......................................................................................................................
- Figure 5 Complete Binary Tree.............................................................................................................
- Figure 6 Dijkstra's table........................................................................................................................
- Figure 7 Shortest Path.........................................................................................................................
- Figure 8 01...........................................................................................................................................
- Figure 9 02...........................................................................................................................................
- Figure 10 03.........................................................................................................................................
- Figure 11 5C 01....................................................................................................................................
- Figure 12 5C 02....................................................................................................................................
- Figure 13 5C 03....................................................................................................................................
- Figure 14 5C 04....................................................................................................................................
- Figure 15 5C 05....................................................................................................................................
- Figure 16 5C 06....................................................................................................................................
- Figure 17 Graph Theory.......................................................................................................................
- Figure 18 EX01.....................................................................................................................................
- Figure 19 Truth table...........................................................................................................................
- Figure 20 Formula Simplified...............................................................................................................
- Figure 21 Circuit...................................................................................................................................
- Figure 22 NAND circuit........................................................................................................................
- Figure 23 (A+C). (B +C). (B+C)..............................................................................................................
- Figure 24 (B + C+D ). (A+B +C+D). (A +B+C). (A +B+D ).........................................................................
- Figure 25 BD + A C + CD + AB + A (B) D
- Figure 26 (B + C+D ). (A+B +C+D). (A +B+C). (A +B+D ).........................................................................
- Figure 27 A C +BC +A B + AB C............................................................................................................
- Figure 28 C +A+B). (C +A +B ). (A +B+C)...............................................................................................
- Figure 29 Binary Operation..................................................................................................................
- Figure 30 1.Operation table.................................................................................................................
- Figure 32 S01.......................................................................................................................................
- Figure 31 S02.......................................................................................................................................
- Figure 34 S03.......................................................................................................................................
- Figure 33 S04.......................................................................................................................................
- Figure 35 S05.......................................................................................................................................
- Figure 36 S06.......................................................................................................................................
- Figure 37 S07.......................................................................................................................................
- Figure 38 S08.......................................................................................................................................
- Figure 39 S09.......................................................................................................................................
- Figure 40 S10.......................................................................................................................................
- Figure 41 S11.......................................................................................................................................
- Figure 42 S12.......................................................................................................................................
- Table 1Process.....................................................................................................................................
- Table 2 Boolean equalization = X.Y.R....................................................................................................
- Table 3 (X ᴧ ~ Y) → Z............................................................................................................................
- Table 4 Boolean Expression.................................................................................................................
- Table 5 Boolean Expression 2..............................................................................................................
- Table 6 NAND.......................................................................................................................................
- Table 7 Truth table...............................................................................................................................
- Table 11Truth table..............................................................................................................................
- n ( A )= 10 + a + 5 + b =
- 15 + a + b =
- a + b = 18
- 20+ a+ c =
- a + c = 16
- b + c= 28 –
- b + c = 10
- a + b = 18
- a + c = 16
- b + c = 10
- 01 – 02 b – c = 2
- 04 + 03 2b = - b =
- 03 c =
- 02 a =
- n ( A ∪ B ∪ C )= 33 + 36 + 28 − 17 − 11 −
N = {1, 2, 3, 4, 5}
Z = {…. -3, -2, -1, 0, 1, 2, 3, 4, 5….}
Z+^ = {1, 2, 3, 4, 5….}
Z-^ = {…. -3, -2, -1,}
I. f^ ( x^ )= x 2
f ( x ) = 2x
f (-3) = 2*(-3) = (-6) → f 2 * (-6) = (-12)
f (-2) = 2*(-2) = (-4) → f 2 * (-4) = (-8)
f (-1) = 2*(-1) = (-2) → f 2 * (-2) = (-4)
f (0) = 2*(0) = (0) → f 2 * (0) = (0)
f (1) = 2*(1) = (2) → f 2 * (2) = (4)
f (2) = 2*(2) = (4) → f 2 * (4) = (8)
f (3) = 2*(3) = (6) → f 2 * (6) = (12)
II.
f ( x )= 1 x 16
f ( 1 )=^1 1 = 1 f ( 2 )= 1 2 f (^1 2 )=^1 1 2 = 2 f ( 3 )= 1 3 f (^1 3 )=^1 1 3 = 3
X 1 , X 2 be two different numbers from domain
f ( x 1 )=^1
x 1 01
f ( x 2 )=^1
x 2 02
f ( x 1 )= f ( x 2 )
x 1
x 2
X 1 = X 2
1-1 function
f ( x )= 1 x
f ( x )= y
Y= 1/x
X=1/y
X → y → x
Y= 1/x (inverse function)
f − 1 ( (^) x ) (^) = 1
x
III. f^ ( x^ )= x 2
x X^2
Function( f^ (^ x^ )= x 2
f ( x )=sin x f :[− π 2 , π 2 ] →[ −1, 1 ] f ( − π 2 )=sin( − π 2 )
= - sin
( π 2 )
f ( π 2 )=sin ( π 2 )
f ( − π 3 )=sin( − π 3 )
= -sin
(
3 ) =−(
√^3
2 ) f ( π 3 )=sin ( π 3 )
=sin
(
3 ) =(
√^3
2 )
Sin 0 = 0 onto function
X 1 , x 2 be two different numbers
f (x 1 ) = sin (x 1 ) 01
f (x 2 ) = sin (x 2 ) 02
Sin (x 1 ) = sin (x 2 ) [ − π 2 , π 2 ]
f (x) = sin (x)
y = f (x)
y = sin (x)
Sin (-x) = - Sin (x)
Sin -1 (y) = x
X → y & y → x
y = sin -1 (x)
f − 1 ( (^) x ) (^) = sin -1(x1) 20
