Exam (elaborations)
COS1501 Assignment 2 (COMPLETE ANSWERS) 2024 (653506) - 14 June 2024
- Course
- Institution
100% TRUSTED WORKINGS, EXPLANATIONS & SOLUTIONS
[Show more]
Seller
Follow
examexpert01
Reviews received
Content preview
COS1501Assignment 2
(COMPLETE
ANSWERS)
2024 (653506) -
14 June 2024
CONTACT: biwottcornelius@gmail.com
, 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. Question 2 Complete
Marked out of 2.00 Question 3 Complete Marked out of 2.00 Let A, B and C
be subsets of a universal set U = {1, 2, 3, 4}. The statement (A – B) U C’ = (C’
– B) + A is NOT an identity. Which of the following sets A, B and C can be
used in a counterexample to prove that the given statement is not an identity?
(Hint: substitute the given sets for LHS and RHS separately) a. A = {1}, B = {2}
and C = {3} b. A = {1}, B = {1} and C = {2} c. A = {1, 2}, B = {1, 2} and C = {3}
d. A = {3}, B = {3, 4} and C = {4} We want to prove that for all A, B, C ⊆ U, (A
⋂ B) U (C – B) = (A U C) ⋂ (A U B’) ⋂ (B U C) is an identity. Consider the
following incomplete proof: z ∈ ( A ⋂ B) U (C – B) iff (z ∈ A and z ∈ B) or ( z ∈
C and z ∉ B) iff (z ∈ A or z ∈ C) and ( z ∈ A or z ∉ B) and (z ∈ B or z ∈ C) and
( z ∈ B or z ∉ B) iff Step 4 iff z ∈ (A U C) and z ∈ (A U B ’ ) and z ∈ (B U C)
and z ∈ (B U B ’ ) iff Step 6 iff z ∈ (A U C) ⋂ (A U B ’ ) ⋂ (B U C) ⋂ U iff z ∈
(A U C) ⋂ (A U B ’ ) ⋂ (B U C) [For any sets U and G, (G ⋂ U) = G.] Which
one of the following alternatives provides valid steps 4 and 6 to complete the
given proof? a. Step 4: iff (z ∈ A or z ∈ C) and (z ∈ A or z ∈ B’) and (z ∈ B or z
∈ C) and (z ∈ B or z ∈ B’ ) Step 6: iff z ∈ (A or C) and z ∈ (A or B’) and z ∈ (B
or C) and z ∈ U b. Step 4: iff (z ∈ A or z ∈ C) and (z ∈ A or z ∈ B’) and (z ∈ B
or z ∈ C) and (z ∈ B or z ∈ B’) Step 6: iff z ∈ (A U C) and z ∈ (A U B’) and z ∈
(B U C) and z ∈ U c. Step 4: iff (z ∈ A or z ∈ C) and (z ∈ A or z ∉ B’) and (z ∈
B or z ∈ C) and (z ∈ B or z ∉ B’) Step 6: iff z ∈ (A U C) or z ∈ (A U B’) or z ∈
(B U C) or z ∈ U d. Step 4: iff (z ∈ A and z ∈ C) or (z ∈ A and z ∈ B’) or (z ∈ B
and z ∈ C) or (z ∈ B and z ∈ B’) Step 6: iff z ∈ (A U C) and z ∈ (A U B’) and z
∈ (B U C) and z ∈ U Question 4 Complete Marked out of 2.00 Question 5
Complete Marked out of 2.00 Forty (40) students go to a party wearing red,
white and blue. Of these students, 17 wear red, 22 wear white, 25 wear blue.
(Students do not necessarily wear only one colour.) Furthermore, 7 wear red
and white, 12 wear blue and white, and 9 wear red and blue . Which one of
the following alternatives is true? (Hint: Draw the Venn diagram, fi ll in the
details given, and then fi rst calculate the value of x, the unknown) a. 5
students wear red only. 8 students wear white and blue, but not red. 3
students wear red and white, but not blue. b. 2 students wear red only. 11
students wear white and blue, but not red. 6 students wear red and white, but
not blue. c. 2 students wear red only. 8 students wear white and blue, but not
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller examexpert01. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.50. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
77764 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now