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COS1501 ASSIGNMENT 3 2021
- Institution
- University Of South Africa (Unisa)
This document contains solutions for COS1501 ASSIGNMENT 3 2021. Working are shown clearly and explanations are provided.
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COS 1501ASSIGNMENT 3 2021
QUESTION 1
𝐿𝑒𝑡: 𝑅 = {(1,3), (𝑏, 3), (1,4), (𝑏, 2), (𝑐, 2)}
𝑅 𝑖𝑠 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑖𝑓 (𝑥, 𝑦) ∈ 𝑅 𝑎𝑛𝑑 (𝑥, 𝑧) ∈ 𝑅 , 𝑡ℎ𝑒𝑛 𝑦 = 𝑧
(1,3) ∈ 𝑅 𝑎𝑛𝑑 (1,4) ∈ 𝑅 𝑡ℎ𝑒𝑛 3 = 4(𝑛𝑜𝑡 𝑡𝑟𝑢𝑒)
𝑅 𝑖𝑠 𝑛𝑜𝑡 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙
ANSWER[1]
QUESTION 2
𝐿𝑒𝑡: 𝑓: 𝑈 → 𝐴 𝑏𝑒 𝑡ℎ𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 {(𝑎, 1), (𝑏, 2), (𝑐, 𝑎), (1,4), (2, 𝑏), (3,3), (4, 𝑐)}
𝑅𝑎𝑛𝑔𝑒 = 𝐴 = {𝑎, 𝑏, 𝑐, 1,2,3,4}
𝑅𝑎𝑛𝑔𝑒 = {𝑎, 𝑏, 𝑐, 1,2,3,4}
𝐶𝑜𝑑𝑜𝑚𝑎𝑖𝑛 = {1,2, 𝑎, 4, 𝑏, 3, 𝑐}
𝐶𝑜𝑑𝑜𝑚𝑎𝑖𝑛 = {1,2, 𝑎, 4, 𝑏, 3, 𝑐} = 𝑅𝑎𝑛𝑔𝑒
𝐶𝑜𝑑𝑜𝑚𝑎𝑖𝑛 = 𝑅𝑎𝑛𝑔𝑒
, 𝑆𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝐶𝑜𝑑𝑜𝑚𝑎𝑖𝑛 = 𝑅𝑎𝑛𝑔𝑒 𝑡ℎ𝑒𝑛, 𝑡ℎ𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑖𝑠 𝑠𝑢𝑟𝑗𝑒𝑐𝑡𝑖𝑣𝑒.
ANSWER:[2]
QUESTION 3
𝐺 𝑎𝑛𝑑 𝐿 𝑎𝑟𝑒 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠 𝑜𝑛 𝐴 = {1,2,3,4}
𝐺 = {(1,2), (2,3), (4,3)} 𝑎𝑛𝑑 𝐿 = {(2,2), (1,3), (3,4)}
𝑡ℎ𝑒𝑛
𝐿 ∘ 𝐺 = {(2,3), (3,3)}
ANSWER:[1]
QUESTION 4
5𝑥 2 + 2𝑥 − 3 > 0
(5𝑥 − 3)(𝑥 + 1) > 0
(5𝑥 − 3) > 0 𝑎𝑛𝑑 (𝑥 + 1) > 0
3
𝑥> 𝑎𝑛𝑑 𝑥 > −1
5
3
𝑥>
5
OR
(5𝑥 − 3) < 0 𝑎𝑛𝑑 (𝑥 + 1) < 0
3
𝑥< 𝑎𝑛𝑑 𝑥 < −1
5
𝑥 < −1
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