Other
COS1501 Assignment 2 2021
- Institution
- University Of South Africa (Unisa)
UNISA COS1501 Theoretical Computer Science Assignment TWO of 2021 solutions.
[Show more]
Content preview
COS1501 Assignment 2 2021Question 1
[(𝐴 ∩ 𝐵)′ − 𝐶] ∩ [(𝐴 + 𝐵) − 𝐶]
𝐴∩𝐵
(𝐴 ∩ 𝐵)′ (𝐴 + 𝐵)
(𝐴 ∩ 𝐵)′ − 𝐶 (𝐴 + 𝐵) − 𝐶
,[(𝐴 ∩ 𝐵)′ − 𝐶] ∩ [(𝐴 + 𝐵) − 𝐶]
Question 1 FOUR
Question 2
𝑈 = {1, 2, 3, 4}
𝐴, 𝐵, 𝐶 𝑎𝑟𝑒 𝑠𝑢𝑏𝑠𝑒𝑡𝑠 𝑜𝑓 𝑈
(𝐴 − 𝐵) ∪ 𝐶 ′ = (𝐶 ′ − 𝐵) + 𝐴
1. 𝐴 = {1}, 𝐵 = {2} 𝑎𝑛𝑑 𝐶 = {3}
𝐿𝐻𝑆 = (𝐴 − 𝐵) ∪ 𝐶 ′
𝐿𝐻𝑆 = (𝐴 − 𝐵) ∪ (𝑈 − 𝐶)
𝐿𝐻𝑆 = ({1} − {2}) ∪ ({1, 2, 3, 4} − {3})
𝐿𝐻𝑆 = {1} ∪ {1, 2, 4}
𝐿𝐻𝑆 = {1, 2, 4}
𝑅𝐻𝑆 = (𝐶 ′ − 𝐵) + 𝐴
𝑅𝐻𝑆 = ((𝑈 − 𝐶) − 𝐵) + 𝐴
𝑅𝐻𝑆 = (({1, 2, 3, 4} − {3}) − {2}) + {1}
𝑅𝐻𝑆 = ({1, 2, 4} − {2}) + {1}
𝑅𝐻𝑆 = {1, 4} + {1}
𝑅𝐻𝑆 = {4}
, 𝐿𝐻𝑆 ≠ 𝑅𝐻𝑆
𝑇ℎ𝑖𝑠 𝑐ℎ𝑜𝑖𝑐𝑒 𝑜𝑓 𝐴, 𝐵 𝑎𝑛𝑑 𝐶 𝑐𝑎𝑛 𝑏𝑒 𝑢𝑠𝑒𝑑 𝑎𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑒𝑟𝑒𝑥𝑎𝑚𝑝𝑙𝑒 𝑡𝑜 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡
(𝐴 − 𝐵) ∪ 𝐶 ′ = (𝐶 ′ − 𝐵) + 𝐴 𝑖𝑠 𝑛𝑜𝑡 𝑎𝑛 𝑖𝑑𝑒𝑛𝑡𝑖𝑡𝑦.
1 is TRUE.
2. 𝐴 = {1}, 𝐵 = {1} 𝑎𝑛𝑑 𝐶 = {2}
𝐿𝐻𝑆 = (𝐴 − 𝐵) ∪ 𝐶 ′
𝐿𝐻𝑆 = (𝐴 − 𝐵) ∪ (𝑈 − 𝐶)
𝐿𝐻𝑆 = ({1} − {1}) ∪ ({1, 2, 3, 4} − {2})
𝐿𝐻𝑆 = ∅ ∪ {1, 3, 4}
𝐿𝐻𝑆 = {1, 3, 4}
𝑅𝐻𝑆 = (𝐶 ′ − 𝐵) + 𝐴
𝑅𝐻𝑆 = ((𝑈 − 𝐶) − 𝐵) + 𝐴
𝑅𝐻𝑆 = (({1, 2, 3, 4} − {2}) − {1}) + {1}
𝑅𝐻𝑆 = ({1, 3, 4} − {1}) + {1}
𝑅𝐻𝑆 = {3, 4} + {1}
𝑅𝐻𝑆 = {1, 3, 4}
𝐿𝐻𝑆 = 𝑅𝐻𝑆
𝑇ℎ𝑖𝑠 𝑐ℎ𝑜𝑖𝑐𝑒 𝑜𝑓 𝐴, 𝐵 𝑎𝑛𝑑 𝐶 𝑐𝑎𝑛𝑛𝑜𝑡 𝑏𝑒 𝑢𝑠𝑒𝑑 𝑎𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑒𝑟𝑒𝑥𝑎𝑚𝑝𝑙𝑒 𝑡𝑜 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡
(𝐴 − 𝐵) ∪ 𝐶 ′ = (𝐶 ′ − 𝐵) + 𝐴 𝑖𝑠 𝑛𝑜𝑡 𝑎𝑛 𝑖𝑑𝑒𝑛𝑡𝑖𝑡𝑦.
2 is FALSE.
3. 𝐴 = {1, 2}, 𝐵 = {1, 2} 𝑎𝑛𝑑 𝐶 = {3}
𝐿𝐻𝑆 = (𝐴 − 𝐵) ∪ 𝐶 ′
𝐿𝐻𝑆 = (𝐴 − 𝐵) ∪ (𝑈 − 𝐶)
𝐿𝐻𝑆 = ({1, 2} − {1, 2}) ∪ ({1, 2, 3, 4} − {3})
𝐿𝐻𝑆 = ∅ ∪ {1, 2, 4}
𝐿𝐻𝑆 = {1, 2, 4}
𝑅𝐻𝑆 = (𝐶 ′ − 𝐵) + 𝐴
𝑅𝐻𝑆 = ((𝑈 − 𝐶) − 𝐵) + 𝐴
𝑅𝐻𝑆 = (({1, 2, 3, 4} − {3}) − {1, 2}) + {1, 2}
𝑅𝐻𝑆 = ({1, 2, 4} − {1, 2}) + {1, 2}
𝑅𝐻𝑆 = {4} + {1, 2}
𝑅𝐻𝑆 = {1, 2. 4}
𝐿𝐻𝑆 = 𝑅𝐻𝑆
𝑇ℎ𝑖𝑠 𝑐ℎ𝑜𝑖𝑐𝑒 𝑜𝑓 𝐴, 𝐵 𝑎𝑛𝑑 𝐶 𝑐𝑎𝑛𝑛𝑜𝑡 𝑏𝑒 𝑢𝑠𝑒𝑑 𝑎𝑠 𝑎 𝑐𝑜𝑢𝑛𝑡𝑒𝑟𝑒𝑥𝑎𝑚𝑝𝑙𝑒 𝑡𝑜 𝑝𝑟𝑜𝑣𝑒 𝑡ℎ𝑎𝑡
(𝐴 − 𝐵) ∪ 𝐶 ′ = (𝐶 ′ − 𝐵) + 𝐴 𝑖𝑠 𝑛𝑜𝑡 𝑎𝑛 𝑖𝑑𝑒𝑛𝑡𝑖𝑡𝑦.
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 EFT, 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 this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lyzo2005. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R150,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
53068 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now