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inklusi-eksklusi pt 2


Soal :
Notasi | A| menyatakan banyaknya elemen himpunan  A. Terdapat sebuah himpunan semesta S dan tiga buah himpunan bagiannya yaitu himpunan X, himpunan Y dan himpunan Z, dimana :

Bila ,

a. Tentukan nilai p

b. Tentukan banyaknya elemen masing-masing himpunan S, X, Y, dan Z.


 

Jawab :

|X| = p + 5 + 2p = 3p + 5

|Y| = 2 ( 3p + 5 ) +1 = 6p + 11

|Z| = 10 + 1 + p = 11 + p

|X U Y U Z | =
9p – 20 = (p+5) + 2p + (3p + 10) + (1 + p) + 10
9p – 20 = 7p + 26
2p = 46
p = 23

|X| = p + 5 + 2p = 3p + 5 = 3 * 23 +5 = 74

|Y| = 2 ( 3p + 5 ) +1 = 6p + 11 = 6 * 23 + 11 = 149

|Z| = 10 + 1 + p = 11 + p = 11 + 23 = 34

|S| = 9p = 9 * 23 = 207.

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