--- BEGIN COPYING --- SLIDE 1 — TITLE ======================================== 2026 MTAP Saturday Program in Grade 7 Mathematics Session 4: SETS Prepared by: Noven N. Nicolas Explained in Taglish for Grade 7 Students 💡 SLIDE 2 — PART A: Well-Defined Sets ======================================== ✅ Well-defined = malinaw kung kasama o hindi. Walang pagtatalo. ❌ Not well-defined = depende sa opinyon ng tao. Well-Defined ✅: 1. Numbers 3. Current senator 5. Barangay Captain aspirant 6. Vowels 9. PBA Players Not Well-Defined ❌: 2. Good looking men 4. Interesting books 7. Presidentiables 8. Pretty woman 10. Candid individuals 11. Super star 12. Respectable man SLIDE 3 — PART B: True or False ======================================== 1. Well-defined set = clear membership → TRUE ✅ 2. Empty set ∅ is subset of all sets → TRUE ✅ 3. L ∈ {L,E,G,A,S,P,I} → TRUE ✅ 4. P = {2,4,6,...,2026} is infinite → FALSE ❌ (finite) 5. Even numbers = multiples of 2 → TRUE ✅ 6. Y−X = elements in Y not in X → TRUE ✅ 7. X∪Y = {1,2,3,4,5,6,7,8,9,10} → FALSE ❌ (no 10) 8. P∩Q = common elements → TRUE ✅ 9. Cardinality = number of elements → TRUE ✅ 10. 3-digit numbers cardinality = 100 → FALSE ❌ (900) SLIDE 4 — PART C: Set Builder → Roster Method ======================================== 1. {x | x integer, 3<x<15} → {4,5,6,7,8,9,10,11,12,13,14} 2. Positive odd integers ≤15 → {1,3,5,7,9,11,13,15} 3. Planets in solar system → {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune} 4. Letters in "STATISTICS" → {S,T,A,I,C} 5. Integers between −10 and +10 → {−9,−8,...,0,...,8,9} 6. Five sense organs → {Eyes, Ears, Nose, Tongue, Skin} SLIDE 5 — PART D: Number of Subsets ======================================== Formula: Number of subsets = 2ⁿ, n = number of elements 1. {1,4,7,10,13}, n=5 → 2⁵ = 32 2. {K,O,R,E,A,N}, n=6 → 2⁶ = 64 3. 1-digit positive {1-9}, n=9 → 512 4. {♦,♣,♥,♠}, n=4 → 16 5. Empty set {}, n=0 → 1 6. Odd integers 4<x<16 = {5,7,9,11,13,15}, n=6 → 64 SLIDE 6 — PART E: Set Operations ======================================== Given: U={2-20}, P=odd, L=even, A=×3, Y=×4, E=×5, R=×6 Symbols Guide: ∪ = Union → pagsasamahin lahat ∩ = Intersection → pareho lang ' = Complement → lahat sa U EXCEPT set − = Difference → sa una lang, wala sa pangalawa Answers: 1. P∪A = {3,5,6,7,9,11,12,13,15,17,18,19} 2. L∪A = {2,3,4,6,8,9,10,12,14,15,16,18,20} 3. A∩R = {6,12,18} 4. Y∩L = {4,8,12,16,20} 5. (P−A)' = U − {5,7,11,13,17,19} 6. (A∪E)' = {2,4,7,8,11,13,14,16,17,19} 7. (P∪R)' = {2,4,8,10,14,15,16,20} 8. (L∪A)' = {5,7,11,13,17,19} 9. (A∩P)' = lahat except {3,9,15} 10. L−E = {2,4,6,8,12,14,16,18} 11. (A−R)' = lahat except {3,9,15} 12. [L∪(E∪R)]' = ∅ 13. P∩(E∪A) = {3,5,9,15} 14. (A∪Y) − (L∩Y) = {3,6,9,15,18} 15. (P−A)∪(L−Y) = {2,3,5,6,7,9,10,11,13,14,15,17,18,19} SLIDE 7 — PART F: Venn Diagrams ======================================== Shaded Region Guide: 1. Outside circle → A' (Complement of A) 2. Part of A not overlapping C → A−C 3. Overlap A and C → A∩C 4. Outside intersection A∩
--- BEGIN COPYING --- SLIDE 1 — TITLE ======================================== 2026 MTAP Saturday Program in Grade 7 Mathematics Session 4: SETS Prepared by: Noven N. Nicolas Explained in Taglish for Grade 7 Students 💡 SLIDE 2 — PART A: Well-Defined Sets ======================================== ✅ Well-defined = malinaw kung kasama o hindi. Walang pagtatalo. ❌ Not well-defined = depende sa opinyon ng tao. Well-Defined ✅: 1. Numbers 3. Current senator 5. Barangay Captain aspirant 6. Vowels 9. PBA Players Not Well-Defined ❌: 2. Good looking men 4. Interesting books 7. Presidentiables 8. Pretty woman 10. Candid individuals 11. Super star 12. Respectable man SLIDE 3 — PART B: True or False ======================================== 1. Well-defined set = clear membership → TRUE ✅ 2. Empty set ∅ is subset of all sets → TRUE ✅ 3. L ∈ {L,E,G,A,S,P,I} → TRUE ✅ 4. P = {2,4,6,...,2026} is infinite → FALSE ❌ (finite) 5. Even numbers = multiples of 2 → TRUE ✅ 6. Y−X = elements in Y not in X → TRUE ✅ 7. X∪Y = {1,2,3,4,5,6,7,8,9,10} → FALSE ❌ (no 10) 8. P∩Q = common elements → TRUE ✅ 9. Cardinality = number of elements → TRUE ✅ 10. 3-digit numbers cardinality = 100 → FALSE ❌ (900) SLIDE 4 — PART C: Set Builder → Roster Method ======================================== 1. {x | x integer, 3<x<15} → {4,5,6,7,8,9,10,11,12,13,14} 2. Positive odd integers ≤15 → {1,3,5,7,9,11,13,15} 3. Planets in solar system → {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune} 4. Letters in "STATISTICS" → {S,T,A,I,C} 5. Integers between −10 and +10 → {−9,−8,...,0,...,8,9} 6. Five sense organs → {Eyes, Ears, Nose, Tongue, Skin} SLIDE 5 — PART D: Number of Subsets ======================================== Formula: Number of subsets = 2ⁿ, n = number of elements 1. {1,4,7,10,13}, n=5 → 2⁵ = 32 2. {K,O,R,E,A,N}, n=6 → 2⁶ = 64 3. 1-digit positive {1-9}, n=9 → 512 4. {♦,♣,♥,♠}, n=4 → 16 5. Empty set {}, n=0 → 1 6. Odd integers 4<x<16 = {5,7,9,11,13,15}, n=6 → 64 SLIDE 6 — PART E: Set Operations ======================================== Given: U={2-20}, P=odd, L=even, A=×3, Y=×4, E=×5, R=×6 Symbols Guide: ∪ = Union → pagsasamahin lahat ∩ = Intersection → pareho lang ' = Complement → lahat sa U EXCEPT set − = Difference → sa una lang, wala sa pangalawa Answers: 1. P∪A = {3,5,6,7,9,11,12,13,15,17,18,19} 2. L∪A = {2,3,4,6,8,9,10,12,14,15,16,18,20} 3. A∩R = {6,12,18} 4. Y∩L = {4,8,12,16,20} 5. (P−A)' = U − {5,7,11,13,17,19} 6. (A∪E)' = {2,4,7,8,11,13,14,16,17,19} 7. (P∪R)' = {2,4,8,10,14,15,16,20} 8. (L∪A)' = {5,7,11,13,17,19} 9. (A∩P)' = lahat except {3,9,15} 10. L−E = {2,4,6,8,12,14,16,18} 11. (A−R)' = lahat except {3,9,15} 12. [L∪(E∪R)]' = ∅ 13. P∩(E∪A) = {3,5,9,15} 14. (A∪Y) − (L∩Y) = {3,6,9,15,18} 15. (P−A)∪(L−Y) = {2,3,5,6,7,9,10,11,13,14,15,17,18,19} SLIDE 7 — PART F: Venn Diagrams ======================================== Shaded Region Guide: 1. Outside circle → A' (Complement of A) 2. Part of A not overlapping C → A−C 3. Overlap A and C → A∩C 4. Outside intersection A∩
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Ang araling ito ay nakatuon sa pag-unawa ng mga set. Magsisimula tayo sa pagkilala sa mga well-defined at not well-defined sets, at pagsusuri ng membership statements. Susunod, tatalakayin ang subsets at set operations gamit ang mga formula at mga halimbawa. Sa huli, gagamitin ang Venn diagrams upang ipakita ang mga relasyon ng sets at ang kanilang mga operasyon. Ang layunin ay gawing malinaw ang bawat konsepto at aplikasyon ng mga set.