Question

Se considera multimile: A={x€N|x=3^n-1, n€N, n<4}, B={y€N*|y=3m-1, m€N, m<_3}. Calculati: AUB, AnB, B-A, AU∅, Bn∅.

Answer 1

A

n=0 x=3^0-1=1-1=0

n=1   x=3^1-1=3-1=2

n=2   x=3^2-1=9-1=8

n=3    x=3^3-1=27-1=26

A={0,2,8,26}

B

m=0 y=3*0-1=0-1=-1∉N

m=1   y=3*1-1=3-1=2

m=2   y=3*2-1=6-1=5

m=3      y=3*3-1=8

B={2,5,8}

AUB={0,2,5,8,26}

A∩B={2,8}

B\A={2,5,8}-{0,2,8,26}={5}

AUФ=A

B∩Ф={2,5,8}∩Ф=Ф