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CONTOH-CONTOH SOAL

CONTOH-CONTOH SOAL. BAB 2 OPERASI HIMPUNAN. 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

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CONTOH-CONTOH SOAL

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  1. CONTOH-CONTOH SOAL BAB 2 OPERASI HIMPUNAN

  2. 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’)’

  3. 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}

  4. U={a,b,c,d,e,f,g} A={a,b,c,d,e} B={a,c,e,g} C={b,e,f,g} • 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

  5. 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’

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

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

  8. Jawab: 3. W-V (arsir miring) U W V W V

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

  10. Jawab: 5. VW’ (arsir miring) U V W W V

  11. Jawab: 6. V‘-W’ (arsir miring) U W W V V

  12. 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

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

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

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

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

  17. Contoh 2.4 : Buktikan persamaan-persamaan berikut : • B – A’ =BA 2. A’- B’=B - A Jawab : • B – A’ ={x|xB, xA’}={x |xB,x  A}= BA 2. A’- B’={x | xA’, xB’}={x|xA,x  B}=B-A

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