1) Determinati multimile
A= (xEz / 8 supra x+2 E N) ( paranteza este in locul acualadei )
B = (xEz / 11 supra 3-x E Z ) (litera "E" inseamna apartine )

2) A=?
A= ( xEN/ /2x+1 / = 3 )
B = ( x E z / / 3x+2 = 5 )

1

Răspunsuri

2014-10-01T23:16:52+03:00
A= (xEz / 8 supra x+2 E N) ( paranteza este in locul acualadei )
x+2∈D8
D8={1,2,4,8}
pt.x+2=1⇒  x=1-2=-1∉N
pt.x+2=2⇒  x=2-2=0∈N
pt.x+2=4⇒  x=2∈N
pt.x+2=8⇒ x=6∈n
deci x∈{0,2,6}


B = (xEz / 11 supra 3-x E Z )  (litera "E" inseamna apartine ) 
3-x∈D11
D11={1,11}
pt.3-x=1⇒  -x=1-3  (-1)⇒x=2∈Z
pt.3-x=11⇒    x=-8∈Z
deci x∈{-8,2}


2) A=?
A= ( xEN/ /2x+1 / = 3 ) 
caz 1: 2x+1=3⇒  2x=3-1⇒ x=4/2=2∈N
caz2  : -2x-1=3⇒  -2x=3+1  (-1)⇒x=-2∉N
sol x∈{2}
B = ( x E z / / 3x+2 = 5 ) 
caz.1:  3x+2=5
⇒ 3x=5-2⇒  3x=3⇒x=1∈Z
caz 2:  -3x-2=5⇒ -3x=5-2⇒-x=3/3  (-1)⇒ x=-1∈Z
deci x∈{-1,1}