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• Theoretical Computer Science
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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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