Roboguru

Diketahui , , dan . Tentukan: d.

Diketahui begin mathsize 14px style S equals left curly bracket 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 right curly bracket end style, begin mathsize 14px style P equals left curly bracket 1 comma space 2 comma space 3 comma space 4 comma space 5 right curly bracket end style, dan begin mathsize 14px style Q equals left curly bracket 2 comma space 4 comma space 6 comma space 7 right curly bracket end style. Tentukan:

d. begin mathsize 14px style P to the power of c union Q to the power of c end style  

Jawaban:

Gabungan dua himpunan begin mathsize 14px style A end style dan size 14px B (begin mathsize 14px style B union A end style) merupakan suatu himpunan yang anggota ialah anggota himpunan begin mathsize 14px style A end style atau anggota himpunan size 14px B atau anggota keduanya.

Suatu komplemen himpunan begin mathsize 14px style A end style (begin mathsize 14px style A to the power of c end style) adalah himpunan yang anggotanya merupakan anggota himpunan semesta tapi bukan anggota begin mathsize 14px style A end style.

Karena:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P to the power of c end cell equals cell open curly brackets 6 comma space 7 comma space 8 comma space 9 comma space 10 close curly brackets end cell row cell Q to the power of c end cell equals cell open curly brackets 1 comma space 3 comma space 5 comma space 8 comma space 9 comma space 10 close curly brackets end cell end table end style 

maka begin mathsize 14px style P to the power of c union Q to the power of c equals open curly brackets 1 comma space 3 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 close curly brackets end style.

Jadi, begin mathsize 14px style P to the power of c union Q to the power of c equals open curly brackets 1 comma space 3 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 close curly brackets end style.

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