Compliment of a set
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This document discusses set complements and provides examples. It defines the complement of a set A as the elements that do not belong to set A. It then gives examples of finding the complement of different sets. For example, if the universal set U is planets in the solar system and set A is {Mercury, Venus, Earth, Mars}, then the complement of A, A', would be {Jupiter, Saturn, Uranus, Neptune}. It concludes with examples of finding the complement of the union and intersection of sets.
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Compliment of a set
- 2. •Set 𝑈 is considered as 𝑈𝑛𝑖𝑣𝑒𝑟𝑠𝑎𝑙 𝑆𝑒𝑡. •It is the set containing all the elements of all other sets. RECALL:
- 3. RECALL:
- 4. COMPLIMENT OF A SET •The complement of a set A, denoted by A’, is the set of elements that does not belong to A.
- 5. EXAMPLE 1 •Consider the sets 𝑈, and 𝐴: 𝑈 = x | x i𝑠 𝑎 𝑝𝑙𝑎𝑛𝑒𝑡 𝑖𝑛 𝑡ℎ𝑒 𝑆𝑜𝑙𝑎𝑟 𝑆𝑦𝑠𝑡𝑒𝑚 𝐴 = 𝑀𝑒𝑟𝑐𝑢𝑟𝑦, 𝑉𝑒𝑛𝑢𝑠, 𝐸𝑎𝑟𝑡ℎ, 𝑀𝑎𝑟𝑠 •What are the planet in the Solar System?
- 6. 𝑈 ={Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune} 𝐴 = 𝑀𝑒𝑟𝑐𝑢𝑟𝑦, 𝑉𝑒𝑛𝑢𝑠, 𝐸𝑎𝑟𝑡ℎ, 𝑀𝑎𝑟𝑠 𝐔 𝐀 ∴ A’={ Jupiter, Saturn, Uranus, Neptune} The Compliment of Set A is the other element of Set U not in Set A.
- 7. EXAMPLE 2 𝑈 = 2, 4, 6, 8, 10, 12 𝐴 = 4, 8, 12 𝐴′ = 2, 6, 10
- 8. EXAMPLE 3 𝑈 = x|x is a letter in the word "honesty" 𝐵 = 𝑡, 𝑜, 𝑦 𝐵′ = ℎ, 𝑛, 𝑒, 𝑠
- 9. Find: 1. A’= 2. B’= 𝑈 = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 𝐴 = 1, 3, 5, 6 𝐵 = 2, 4, 5, 6 EXAMPLE 4 0, 2, 4, 7, 8, 9 0, 1, 3, 7, 8, 9
- 10. Find: 3. (A∪B)’= 4. (A∩B)’= 𝑈 = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 𝐴 = 1, 3, 5, 6 𝐵 = 2, 4, 5, 6 1, 2, 3, 4, 5, 6 ′ 5, 6 ’ = 𝟎, 𝟕, 𝟖, 𝟗 = 𝟎, 𝟏, 𝟐, 𝟑, 𝟒, 𝟕, 𝟖, 𝟗
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