Question

scrieti elementele multimii  M9 intersectie  D36

c)  scrieti prin enumerare elementele multimii B={ n∈N / 3 < 2n + 1 ≤ 33

    stability valoarea de adevar a propozitiilor

f) 17∈ {13,14,15 , ... , 21 } intersectie { 2,4,6, ... , 32 }

exista numere natural n astel incat multimile C= { 4x + 1 , 12 , 27 }  si  D= { 4x , 4x + 2 , 2x + 7 } sa aiba doua elemenete commune ? justificati raspunsul .

Answer 1

M9={0,9,18,27,36,45,54,63,72,81,90....}
D36=[1,2,3,4,6,9,12,18,36}
M9inters.D36={9,18,36}

c)3<2n+1
3-1<2n
2<2n
-2n<-2      (-1)
2n>2
n>2/2
n>1

2n+1≤33
2n≤33-1
n≤32/2
n≤16
B={2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}

f){13,14,15,16,....21}inters.{2,4,6,...32}={14,16,18,20,22,...32}
17∈Ф

dam valori lui x
x=1⇒C={5,12,27} si D={4,6,9} nu au nici un element comun
x=2⇒C={9,12,27} si D={8,10,11} idem
x=3⇒C={13,12,27 si D={12,14,13} au element comun pe 12
x=4⇒C={17,12,27} siD={16,18,15} nici un elem
x=5 idem
x=6 idem
x=7 idem
x=8⇒C={33,12,27} si D={32,34,23} nici un elem
x=9⇒idem
x=10⇒C={41,12,27} si D={40,42,27} element comun 27
singurele  elem comun sunt 12 si 27
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