1. Ways of defining a set Lecture no. 2

2. 1.) THE ROSTER NOTATION OR LISTING METHOD is a method describing a set by listing each element of the set inside the symbol { }.

3. Examples: 1.A={1,2,3,4} 2.B={p,h,i,l,i, p,p,i,n,e,s} 3.C={5,10,15,…} 4.D = {a, e, i, o, u} 5.E = { pinky, ring, middle, index, thumb}

4. 2.) THE VERBAL DESCRIPTION METHOD Examples: 1.Set A is the set of counting numbers less than 5 2. Set B is the set of distinct letters in the word “Philippines” 3.Set C is the set of positive multiples of 5.

5. 4.Set D is the set of all Vowels in the alphabet 5.Set E is the set of names of fingers

6. 3. THE SET BUILDER NOTATION 1. A ={x | x is a counting number less than 5} read as “ the set of all x’s such that x is a counting number less than 5.” The vertical bar after the first x s translated as “such that.”

7. 2. B={x | x is the distinct letters in the word “Philippines.”} 3. C={ x | x is a positive multiple of 5} 4. Set D ={ x | x is all vowels in the alphabet. 5. Set E = { x | x is the names of fingers

8. SEATWORK NO. 2 Write LM for listing Method, VDM for Verbal Description Method and SBN for Set Builder Notation for the following set

9. 1.R = {set of all vowels in the alphabet} 2.P = { 1, 3, 5, 7, …} 3.Set R is the set of all vowels in the English Alphabet 4.A = {mango, apple, banana, pineapple, grapes} 5.D = {fingers}

10. 6.X = { x | x is the set of all trees} 7.Set Z is the set of all trees in the Philippines 8.O = { cow, dog, cat, goat} 9.U = { } 10. P = {x | x is the set of Presidents of the Philippines}

11. ANSWER 1.VDM 2.LM 3.VDM 4.LM 5.VDM 6.SBN 7.VDM 8.LM 9.LM 10.SBN

12. QUIZ NO. 2 Choose the letter of the correct answer

13. 1. WHICH OF THE FOLLOWING IS A SET BUILDER NOTATION? A. A = {a, b, c, d} B. B = { x I x is the set of all counting numbers} C. C = {bananas, mangoes, grapes, oranges} D. D = {Fruit Trees}

14. 2. THE FOLLOWING EXAMPLES ARE LISTING METHOD EXCEPT A. A = { 1, 2, 3,..} B. B = { } C. C = { a, e, i, o, u} D. Set D is the set of all counting numbers less than 20

15. 3. WHAT TYPE OF SET IS SET A = {1, 2, 3, …} A. Infinite B. Finite C. Subset D. Proper subset

16. 4. WHICH OF THE FOLLOWING IS A PROPER SUBSET OF P = { A, B, C, D E } A. A = { A, B, E} B. B = { A, B, C, D} C. C = { A, B, C, D, E, F} D. D = { C, D, E}

17. 5. WHICH OF THE FOLLOWING IS THE EQUAL SET OF A = { E, A, R, T, H } A. A = { A, R, C, S } B. B = { S, C, A, R } C. C = { H, E, A, R, T,} D. D = { R, A, C, S }

19. ANSWER KEY 1. B 2. D 3. A 4. C 5. C