Question

Determinati:A={x€Z/ 12supra x+1€Z};B={x€Z/ -20 supra 2x+3€N};C={(x,y)€ZoriZ/xy=-8};D={x€Z/4<|x|<8}

Answer 1

a)  x+1∈D(12)
D(12)={1,2,3,4,6,12}
x+1=1⇒x=0∈Z
x+1=2⇒x1∈Z
x+1=3⇒x=2∈Z
x+1=4⇒x=3∈Z
x+1=6⇒x=5∈Z
x+1=12⇒x=11∈Z
deci X∈{0,1,2,3,5,11}

B) 2X+3∈D(-20)
D(-20)={-1,-2,-4,-5,-10,-20}
2X+3=-1⇒2X=-4⇒X=-2∉N
2X+3=-2⇒2X=-5⇒X=-5/2∉N
2X+3=-4⇒2X=-7⇒X=-7/2∉N
2X+3=-5⇒X=-4∉N
2X+3=-10⇒X=-13/2∉N
2X+3=-20⇒X=-23/2∉N
DECI X∈Ф

D)X<8 SI X>4
X=5∈Z
X=6∈Z
X=7∈Z
DECI X∈{5,6,7}