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OPERASI-OPERASI HIMPUNAN

OPERASI-OPERASI HIMPUNAN. GABUNGAN ( Union ) IRISAN ( Intersection ) SELISIH( Difference ) KOMPLEMEN ( Complement ). GABUNGAN . A B={x |xA atau x B atau x A dan B }. U. A. B. U = himpunan Semesta. A B bagian yang diarsir horisontal. Contoh :

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OPERASI-OPERASI HIMPUNAN

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  1. OPERASI-OPERASI HIMPUNAN • GABUNGAN (Union) • IRISAN (Intersection) • SELISIH(Difference) • KOMPLEMEN (Complement)

  2. GABUNGAN  • AB={x|xA atau x B atau x A dan B } U A B U = himpunan Semesta AB bagian yang diarsir horisontal Contoh : S={a,b,c,d} T={f,b,d,g} ST={a,b,c,d,f,g} =T S

  3. Contoh : S={a,b,c,d} T={f,b,d,g} ST={a,b,c,d,f,g}

  4. A AB B IRISAN  • AB={x|xA dan x B} U AB bagian yang diarsir horisontal dan vertikal Contoh : S={a,b,c,d} T={f,b,d,g} ST={b,d} = TS

  5. SELISIH - U • A-B={x|xA dan x B } A B B A-B bagian yang diarsir horisontal Contoh : S={a,b,c,d} T={f,b,d,g} S-T={a,c}  T-S={f,g}

  6. KOMPLEMEN A=A’ U • A’={x|x  A} =U-A U A A A’ bagian yang diarsir horisontal Contoh : U={x|x=alfabet} S={a,b,c,d} S’={e,f,g,h,…….,x,y,z}

  7. B A A OPERASI PADA HIMPUNAN Comparable • AB atau B A  A dan B comparable • Bila AB AB = A AB bagian yang diarsir horisontal dan vertikal  A

  8. B A A • Bila AB AB = B AB bagian yang diarsir horisontal  B

  9. B B A A A • Bila AB = B’ A’ A’diarsir horisontal B’diarsir horisontal

  10. Contoh 2.1: Misalkan diketahui himpunan-himpunan U, A,B,C : U={a,b,c,d,e,f,g} A={a,b,c,d,e} B={a,c,e,g} C={b,e,f,g} • Tentukan : • AC 2. BA 3. C-B 4. B’ 5.A’-B • B’ C 7. (A-C)’ 8. C’ A 9.(A-B’)’ 10. (A A’)’

  11. Jawab : U={a,b,c,d,e,f,g} A={a,b,c,d,e} B={a,c,e,g} C={b,e,f,g} • AC ={a,b,c,d,e,f,g}=U • BA ={a,c,e} • C-B={b,f} • B’ ={b,d,f} • A’-B ={f}

  12. B’ C ={b,d,e,f,g} • (A-C)’ = {b,e,f,g} • C’ A = {a,c,d} • (A-B’)’ = {b,d,f,g} • (A A’)’ = U

  13. Contoh 2.2: Diketahui diagram Venn : U V W • Lakukan arsir pada himpunan-himpunan berikut : • V  W 2. W’ 3. W-V 4. V’ W 6.A’-W’

  14. Jawab: 1. V  W (arsir kotak) U W V

  15. Jawab: 2. W’ (arsir miring) U W V

  16. Jawab: 3. W-V (arsir miring) U W V • Lakukan arsir pada himpunan-himpunan berikut : • V  W 2. W’ 3. W-V 4. V’ W 6.A’-W’

  17. Jawab: 4. V’W (arsir miring) U W V

  18. Jawab: 5. VW’ (arsir miring) U W V • Lakukan arsir pada himpunan-himpunan berikut : • V  W 2. W’ 3. W-V 4. V’ W 6.A’-W’

  19. Jawab: 6. V‘-W’ (arsir miring) U W V • Lakukan arsir pada himpunan-himpunan berikut : • V  W 2. W’ 3. W-V 4. V’ W 6.A’-W’

  20. Contoh 2.3: Gambarkan diagram Venn untuk tiga himpunan A, B dan C yang tidak kosong () bila diketahui : • AB, C B, AC =  • A  B, CB, AC  • A  C, A  C, BC =  • A (B  C), B C, C  B,A C

  21. Jawab: • AB, C B, AC =  B C A

  22. Jawab: • A  B, CB, AC  C A B

  23. Jawab: • A  C, A  C, BC =  C B A

  24. Jawab: • A (B  C), B C, C  B,A C C A B

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