(J) RICHFIELD

MATHEMATICS 511 FACULTY OF INFORMATION TECHNOLOGY

Name & Surname:ICAS / ITS No:

Qualification:Semester:Module Name:

Date Submitted:

ASSESSMENT CRITERIA MARK ALLOCATION EXAMINER MARKS MODERATOR MARKS

MARKS FOR CONTENT

QUESTION ONE

1.1 10

1.2 10

1.3 10

1.4 10

1.5 10

1.6 20

1.7 10

1.8 10

1.9 10

TOTAL MARKS FOR ASSIGNMENT 100

Examiner’s Comments:

Moderator’s Comments:

Signature of Examiner: Signature of Moderator:

ASSIGNMENT INSTRUCTIONS

1. All assignment must be typed, not handwritten.

2. Every assignment should include the cover page, table of contents and a reference list or bibliography at the end of the document

3. A minimum of five current sources (references) should be used in all assignments and these should reflect in both in-text citations as well as the reference list or bibliography

4. In-text citations and a reference list or bibliography must be provided. Use the Harvard Style for both in-text citations and the reference list or bibliography

5. Assignments submitted without citations and accompanying reference lists will be penalised.

6. Students are not allowed to share assignments with fellow students. Any shared assignments will attract stiff penalties.

7. The use of, and copying of content from websites such as chegg.com, studocu.com, transtutors.com, sparknotes.com or any other assignment-assistance websites is strictly prohibited. This also applies to Wiki sites, blogs and YouTube.

8. Any pictures and diagrams used in the Assignment should be properly labelled and referenced.

9. Correct formatting as indicated on the Cover Page should be followed (font-size 12, font-style Calibri, line spacing of 1.0 and margins justified)

10. All Assignments must be saved in PDF using the correct naming-convention before uploading on Moodle. Eg StudentNumber_CourseCode_Assignment (402999999_WBT512A_Assignment).

QUESTIONS

MARKS

1.1 Construct the truth table of the given compound proposition

(PV q) A (q V s) ^ (—r V p) A (q V s) [10]

1.2 Use only the property of the logical equivalences to prove that

(P ^ — q)A(p^ — r) = —(p A (q V r)) [10]

1.3 Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces

the output ((—p V —r) A —q) V (—p A (q V r)) from input bits p, q and r. [10]

1.4 Given the U = {21,22,23,24,25,26,27,28,29,30} and

A = {23,24,25,26,27}

B = {21,25,27,29}

C = {23,26,29}

D = {22,24,26,28}.

Find

a. Ac nBc [2]

b. (4 u C) n (B u D) [2]

c. (A — D) U (B — D) [2]

d. (A n C)c U (B U D)c [2]

e. (D — C) n (B — 4)c [2]

1.5 a. In an arithmetic progression the sum of the first ten terms is 400 and the sum

of the next term is 1000. Find the common difference and the first term. [5]

b. The seventh term and the twelfth term of an arithmetic progression are 28 and

73, respectively.

i. Find the first term and the common difference of the progression.

ii. Calculate the sum of the first forty terms of the progression. [5]

1.6 Solve the following equation using 7% - 8y + 5z = 5

—4x + 5y — 3z = —3

x — y + z = 0

a. Crammer’s rule

b. Inverse Method

13

1.7 2 1

40

—1

13

03

—3 7

7

1

1

Find the matrix A.

[10]

[10]

[10]

x-4

1.8 Given: f(x) = 3x + k and g(x) = —— For what value of k is f(g(x)) = g(f(x))

[10]

1.9 Solve the traveling salesperson problem for this graph by finding the total weight of all Hamilton circuits and determining a circuit with minimum total weight. [10]

? 3 j5

MATHEMATICS 511 FACULTY OF INFORMATION TECHNOLOGY

Name & Surname:ICAS / ITS No:

Qualification:Semester:Module Name:

Date Submitted:

ASSESSMENT CRITERIA MARK ALLOCATION EXAMINER MARKS MODERATOR MARKS

MARKS FOR CONTENT

QUESTION ONE

1.1 10

1.2 10

1.3 10

1.4 10

1.5 10

1.6 20

1.7 10

1.8 10

1.9 10

TOTAL MARKS FOR ASSIGNMENT 100

Examiner’s Comments:

Moderator’s Comments:

Signature of Examiner: Signature of Moderator:

ASSIGNMENT INSTRUCTIONS

1. All assignment must be typed, not handwritten.

2. Every assignment should include the cover page, table of contents and a reference list or bibliography at the end of the document

3. A minimum of five current sources (references) should be used in all assignments and these should reflect in both in-text citations as well as the reference list or bibliography

4. In-text citations and a reference list or bibliography must be provided. Use the Harvard Style for both in-text citations and the reference list or bibliography

5. Assignments submitted without citations and accompanying reference lists will be penalised.

6. Students are not allowed to share assignments with fellow students. Any shared assignments will attract stiff penalties.

7. The use of, and copying of content from websites such as chegg.com, studocu.com, transtutors.com, sparknotes.com or any other assignment-assistance websites is strictly prohibited. This also applies to Wiki sites, blogs and YouTube.

8. Any pictures and diagrams used in the Assignment should be properly labelled and referenced.

9. Correct formatting as indicated on the Cover Page should be followed (font-size 12, font-style Calibri, line spacing of 1.0 and margins justified)

10. All Assignments must be saved in PDF using the correct naming-convention before uploading on Moodle. Eg StudentNumber_CourseCode_Assignment (402999999_WBT512A_Assignment).

QUESTIONS

MARKS

1.1 Construct the truth table of the given compound proposition

(PV q) A (q V s) ^ (—r V p) A (q V s) [10]

1.2 Use only the property of the logical equivalences to prove that

(P ^ — q)A(p^ — r) = —(p A (q V r)) [10]

1.3 Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces

the output ((—p V —r) A —q) V (—p A (q V r)) from input bits p, q and r. [10]

1.4 Given the U = {21,22,23,24,25,26,27,28,29,30} and

A = {23,24,25,26,27}

B = {21,25,27,29}

C = {23,26,29}

D = {22,24,26,28}.

Find

a. Ac nBc [2]

b. (4 u C) n (B u D) [2]

c. (A — D) U (B — D) [2]

d. (A n C)c U (B U D)c [2]

e. (D — C) n (B — 4)c [2]

1.5 a. In an arithmetic progression the sum of the first ten terms is 400 and the sum

of the next term is 1000. Find the common difference and the first term. [5]

b. The seventh term and the twelfth term of an arithmetic progression are 28 and

73, respectively.

i. Find the first term and the common difference of the progression.

ii. Calculate the sum of the first forty terms of the progression. [5]

1.6 Solve the following equation using 7% - 8y + 5z = 5

—4x + 5y — 3z = —3

x — y + z = 0

a. Crammer’s rule

b. Inverse Method

13

1.7 2 1

40

—1

13

03

—3 7

7

1

1

Find the matrix A.

[10]

[10]

[10]

x-4

1.8 Given: f(x) = 3x + k and g(x) = —— For what value of k is f(g(x)) = g(f(x))

[10]

1.9 Solve the traveling salesperson problem for this graph by finding the total weight of all Hamilton circuits and determining a circuit with minimum total weight. [10]

? 3 j5

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