Question

8. Determinați elementele mulțimilor: A = {neN/n/n +9),
B={neN/ n +1/n + 6), C = {neN/2n + 1/2n +8},
D = {neN/n-3/n), E = {neN/2n + 1/5n+8). vă implorrrrr !!!!
dau coroană ​

Answer 1

A={n∈N/ n/n+9}

n/n+9

n/n   (-)

=> n/n+9-n,  n/9 => n∈{1, 3, 9}

A={1, 3, 9}

B={n∈N/ n+1/n+6}

n+1/n+6

n+1/n+1  (-)

=> n+1/n+6-(n+1)

n+1/5 => n+1∈{1, 5}=> n∈{0, 4}

B={0, 4}

C={n∈N/ n-3/n}

n-3/n

n-3/n-3   (-)

=> n-3/n-(n-3)

n-3/3 => n-3∈{1, 3}; n∈{4, 6}

C={4, 6}

D={n∈N/ 2n+1/5n+8}

2n+1/5n+8   /*2

2n+1/2n+1   /*5

=> 2n+1/10n+16

   2n+1/10n+5 (-)

=> 2n+1/11 => 2n+1∈{1, 11}

2n∈{0, 10} => n∈{0,5}

D={0, 5}