Exam (elaborations)

Exam (elaborations) COS1501 Assignment 2 (COMPLETE ANSWERS) 2024 (653506) - 14 June 2024 • Course • Theoretical Computer Science I (COS1501) • Institution • University Of South Africa (Unisa) • Book • Theoretical Computer Science COS1501 Assignment 2 (COM

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Course
COS1501

Institution
University Of South Africa

Book
Theoretical Computer Science

Exam (elaborations) COS1501 Assignment 2 (COMPLETE ANSWERS) 2024 (653506) - 14 June 2024 • Course • Theoretical Computer Science I (COS1501) • Institution • University Of South Africa (Unisa) • Book • Theoretical Computer Science COS1501 Assignment 2 (COMPLETE ANSWERS) 2024 (653...

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Uploaded on June 14, 2024
Number of pages 35
Written in 2023/2024
Type Exam (elaborations)
Contains Questions & answers

cos1501

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COS1501
Assignment
2
• Theoretical Computer
Science I (COS1501)
• Theoretical Computer Science
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, Exam (elaborations)
COS1501 Assignment 2 (COMPLETE ANSWERS) 2024
(653506) - 14 June 2024
Course

 Theoretical Computer Science I (COS1501)
 Institution
 University Of South Africa (Unisa)
 Book
 Theoretical Computer Science

COS1501 Assignment 2 (COMPLETE ANSWERS) 2024 (653506) - 14 June
2024; 100% TRUSTED workings, explanations and solutions. ........

Question 1 Complete Marked out of 2.00 Let A, B and C be subsets of a
universal set U. Which one of the following four Venn diagrams presents the
set [(A ⋂ B) ’ – C] ⋂ [( A + B) – C ] ? (Hint: Draw the Venn diagrams for [(A ⋂
B) ’ – C] ⋂ [( A + B) – C ] step by step). a. b. c. d.


Step-by-Step Solution:

1. [(A ⋂ B)']: The complement of the intersection of sets A and B

 Draw sets A and B.
 Shade the region outside the intersection of A and B (everything except the intersection).

2. [(A ⋂ B)' - C]: Remove the region of set C from the complement of (A ⋂ B)

 From the shaded area obtained in Step 1, remove the region that belongs to set C.

3. [(A + B) – C]: The union of sets A and B, minus set C

 Draw sets A and B.
 Shade the region inside A or B, but outside C.

4. [(A ⋂ B)’ – C] ⋂ [(A + B) – C]: Intersection of the shaded areas from Steps 2 and 3

,  Find the common region in the shaded areas obtained from Steps 2 and 3.

Let's go through each of these steps visually.

Step 1: [(A ⋂ B)']

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- Everything outside the intersection of A and B.

Step 2: [(A ⋂ B)' - C]

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- Remove set C from the shaded area obtained in Step 1.

Step 3: [(A + B) – C]

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- Everything inside A or B, but outside C.

Step 4: [(A ⋂ B)’ – C] ⋂ [(A + B) – C]

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- Intersection of the shaded areas from Steps 2 and 3.

Now, let's illustrate each step:

Step 1: [(A ⋂ B)'] and Step 2: [(A ⋂ B)' - C]

Let's draw and shade the regions outside the intersection of A and B, and then remove set C from
it.

Step 3: [(A + B) – C]

Let's draw sets A and B again, and shade the region inside A or B, but outside C.

Step 3: [(A + B) – C]

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- Everything inside A or B, but outside C.
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