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Pertanyaan

Perhatikan pernyataan-pernyataan berikut! i) AC + DB = AB + DC ii) AC + BC = BD + AD Pernyataan yang bernilai benar ditunjukkan oleh nomor ....

Perhatikan pernyataan-pernyataan berikut!

i)     

ii)     

Pernyataan yang bernilai benar ditunjukkan oleh nomor ....

  1. i) saja

  2. ii) saja

  3. i) dan ii)

  4. tidak keduanya

  5. tidak dapat disimpulkan

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I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

jawaban yang tepat adalah A.

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Pembahasan

Perhatikan bahwa jika dan hanya jika . Kemudian perhatikan pernyataan pertama. i) Misalkan dan . Perhatikan bahwa Karena , maka atau . Maka pernyataan i) bernilai benar. Selanjutnya perhatikan pernyataan kedua. ii) Misalkan dan . Perhatikan bahwa Karena , maka atau . Maka pernyataan ii) bernilai salah. Sehingga pernyataan yang bernilai benar ditunjukkan oleh nomor i) saja. Jadi, jawaban yang tepat adalah A.

Perhatikan bahwa begin mathsize 14px style straight p with rightwards arrow on top equals straight q with rightwards arrow on top end style jika dan hanya jika begin mathsize 14px style straight p with rightwards arrow on top minus straight q with rightwards arrow on top equals 0 with rightwards arrow on top end style.

 

Kemudian perhatikan pernyataan pertama.

i)    begin mathsize 14px style AC with rightwards arrow on top plus DB with rightwards arrow on top equals AB with rightwards arrow on top plus DC with rightwards arrow on top end style

Misalkan begin mathsize 14px style straight p with rightwards arrow on top equals AC with rightwards arrow on top plus DB with rightwards arrow on top end style dan begin mathsize 14px style straight q with rightwards arrow on top equals AB with rightwards arrow on top plus DC with rightwards arrow on top end style.

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight p with rightwards arrow on top minus straight q with rightwards arrow on top end cell equals cell open parentheses AC with rightwards arrow on top plus DB with rightwards arrow on top close parentheses minus open parentheses AB with rightwards arrow on top plus DC with rightwards arrow on top close parentheses end cell row blank equals cell AC with rightwards arrow on top plus DB with rightwards arrow on top minus AB with rightwards arrow on top minus DC with rightwards arrow on top end cell row blank equals cell AC with rightwards arrow on top minus DC with rightwards arrow on top plus DB with rightwards arrow on top minus AB with rightwards arrow on top end cell row blank equals cell AC with rightwards arrow on top minus open parentheses negative CD with rightwards arrow on top close parentheses plus DB with rightwards arrow on top minus open parentheses negative BA with rightwards arrow on top close parentheses end cell row blank equals cell AC with rightwards arrow on top plus CD with rightwards arrow on top plus DB with rightwards arrow on top plus BA with rightwards arrow on top end cell row blank equals cell AA with rightwards arrow on top end cell row blank equals cell 0 with rightwards arrow on top end cell end table end style

Karena begin mathsize 14px style straight p with rightwards arrow on top minus straight q with rightwards arrow on top equals 0 with rightwards arrow on top end style, maka begin mathsize 14px style straight p with rightwards arrow on top equals straight q with rightwards arrow on top end style atau begin mathsize 14px style AC with rightwards arrow on top plus DB with rightwards arrow on top equals AB with rightwards arrow on top plus DC with rightwards arrow on top end style.

Maka pernyataan i) bernilai benar.

 

Selanjutnya perhatikan pernyataan kedua.

ii)    begin mathsize 14px style AC with rightwards arrow on top plus BC with rightwards arrow on top equals BD with rightwards arrow on top plus AD with rightwards arrow on top end style

Misalkan begin mathsize 14px style straight p with rightwards arrow on top equals AC with rightwards arrow on top plus BC with rightwards arrow on top end style dan begin mathsize 14px style straight q with rightwards arrow on top equals BD with rightwards arrow on top plus AD with rightwards arrow on top end style.

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight p with rightwards arrow on top minus straight q with rightwards arrow on top end cell equals cell open parentheses AC with rightwards arrow on top plus BC with rightwards arrow on top close parentheses minus open parentheses BD with rightwards arrow on top plus AD with rightwards arrow on top close parentheses end cell row blank equals cell AC with rightwards arrow on top plus BC with rightwards arrow on top minus BD with rightwards arrow on top minus AD with rightwards arrow on top end cell row blank equals cell AC with rightwards arrow on top minus AD with rightwards arrow on top plus BC with rightwards arrow on top minus BD with rightwards arrow on top end cell row blank equals cell AC with rightwards arrow on top minus open parentheses negative DA with rightwards arrow on top close parentheses plus BC with rightwards arrow on top minus open parentheses negative DB with rightwards arrow on top close parentheses end cell row blank equals cell AC with rightwards arrow on top plus DA with rightwards arrow on top plus BC with rightwards arrow on top plus DB with rightwards arrow on top end cell row blank equals cell DA with rightwards arrow on top plus AC with rightwards arrow on top plus DB with rightwards arrow on top plus BC with rightwards arrow on top end cell row blank equals cell open parentheses DA with rightwards arrow on top plus AC with rightwards arrow on top close parentheses plus open parentheses DB with rightwards arrow on top plus BC with rightwards arrow on top close parentheses end cell row blank equals cell DC with rightwards arrow on top plus DC with rightwards arrow on top end cell row blank equals cell 2 DC with rightwards arrow on top end cell end table end style 

Karena begin mathsize 14px style straight p with rightwards arrow on top minus straight q with rightwards arrow on top not equal to 0 end style, maka begin mathsize 14px style straight p with rightwards arrow on top not equal to straight q with rightwards arrow on top end style atau begin mathsize 14px style AC with rightwards arrow on top plus BC with rightwards arrow on top not equal to BD with rightwards arrow on top plus AD with rightwards arrow on top end style.

Maka pernyataan ii) bernilai salah.

 

Sehingga pernyataan yang bernilai benar ditunjukkan oleh nomor i) saja.

Jadi, jawaban yang tepat adalah A.

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