Question

Buna ! Ma ajutati va rog si pe mine la problema? 
1. Se  considera multimile E: { x∈NΙ 25 la puterea x <125⁷ : 5⁹} si F={ y∈N*Ι y=5-x,x∈E} a) Nominalizati elementele multimii E
Nominalizati elementele multimii F
Determinati EυF, E intersectat cu F, E/F SI F/E

Answer 1

$25^{x} < \frac{ 125^{7} }{ 5^{9} } <=> 5^{2x} < \frac{ 5^{21} }{ 5^{9} } <=> 5^{2x} < 5^{12}$

2x < 12
x < 6
E = {0; 1; 2; 3; 4; 5}
F = {(5-0); (5-1)....(5-5)}  
F = {0; 1; 2; 3; 4; 5}
=> E = F
E U F = E = F
E ∩ F = E = F
E / F  = Ф
F / E = Ф

Answer 2

25 ^x = (5²)^x

125⁷=(5³)⁷= 5²¹

5²¹ :5⁹= 5¹⁸

5²x < 5¹⁸

2x < 18 |:2

x < 9  
x∈N    ⇒x∈{1,2,3,4,5,6,7,8}

E={1,2,3,4,5,6,7,8}

y=5-x

y=5-1=4
y=5-2=3
y=5-3=2
y=5-4=1
y=5-5=0
y=5-6=-1
y=5-7=-2
y=5-8=-3

y∈N*  ⇒y∈{1,2,3,4}

a)E u F={1,2,3,4,5,6,7,8}

E intersectat F= {1,2,3,4}

E/F={Ф}

F/E={5,6,7,8}