Question

1.Determina elementele multimii M={x €N*|20 supra 3x-2€N}.
2.Determina mulțimile A si B,stiind ca AUB={1,2,3,4,5},A intersectat cu B={2,4} si A-B={1,5}.
Va rog ajutati-ma!

Answer 1

1.20/(3x-2) ∈ N
=> 3x-2 ∈ D20:{1,2,4,5,10,20}
3x-2=1=> 3x=3=> x=1
3x-2=2=> 3x=4-> nu convine
3x-2=4=>3x=6=> x=2
3x-2=5=> 3x=7->nu convine
3x-2=10=>3x=12=> x=4
3x-2=20=> 3x=22-> nu convine
=> M={1,2,4}

2.AUB={1,2,3,4,5}
A∩B={2,4}
A/B={1,5}
AUB=A∩B+A/B+B/A
=> B/A={3}
=> A={1,2,4,5}
B={2,3,4}