Question

A={x E N\21<5 (3x-3)+4+3(2x-4)}
B={x E N\11<3(2x-3)-6≤ 65}
a)sa se dedermine multimile AsiB
b)sa se afleAUB,AnB,A-B,B-A
c)dederminati cardinalul(AUB) ≤cardinalul A+cardinalul B

Answer 1

a)
B=
11<3(2x−3)−6≤65
11<6x−15≤65
11+15<6x−15+15≤65+15 Aduni 15 in ambii termeni
26<6x≤80
26/6<6x/6≤80/6 
13/3<x≤40/3

13/3=4,(3)
40/3=13,(3) 
x∈ℕ=> x∈ {5,6,7,...,13}

A=
21<5(3x−3)+4+3(2x−4)
21<21x−23
21x−23>21
21x−23+23>21+2321x>44
x>44/21

44/21=~2,1
x∈ℕ=> x∈ {3,4,5,...}