Question

Fie mulțimile
A={n/n€N,n=5^a+2^b,unde a€(0,2),b€(1,2,3)}
B={x/x € N,x=3×n-1,unde n€A}
C={p/p € N,p=m^2 -3,unde m€B}

Scrieţi mulțimile prin enumerarea elementelor(adică cu cifre)

€=aparține
^=la puterea
N=numere naturale

DAU COROANĂ! URGENT VĂ ROG​

Answer 1

A={n / n€N, n=5^a+2^b}

a€{0, 2}

b€{1, 2, 3}

a=0, b=1 => n=5^0+2^1=2

a=0, b=2 => n=5^0+2^2=4

a=0, b=3 => n=5^0+2^3=8

a=2, b=1 => n=5^2+2^1=25+2=27

a=2, b=2 => n=5^2+2^2=25+4=29

a=2, b=3 => n=5^2+2^3=25+8=33

A={2, 4, 8, 27, 29, 33}

B={x / x€N, x=3n-1, n€A}

n=2 => x=3•2-1=6-1=5

n=4 => x=3•4-1=12-1=11

n=8 => x=3•8-1=24-1=23

n=27 => x=3•27-1=81-1=80

n=29 => x=3•29-1=87-1=86

n=33 => x=3•33-1=99-1=98

B={5, 11, 23, 80, 86, 98}

C={p / p€N, p=m^2-3, m€B}

m=5 => p=5^2-3=25-3=22

m=11 => p=11^2-3=121-3=118

m=23 => p=23^2-3=529-3=526

m=80 => p=80^2-3=6400-3=6397

m=86 => p=86^2-3=7396-3=7393

m=98 => p=98^2-3=9604-3=9601

C={22, 118, 526, 6397, 7393, 9601}