Question

Care este cardinalul multimii M={x|x apartine lui N,x=3n -4,n apartine N,x<25}
Dau 20 de pct la raspunsul corect şi cel mai repede
Va rog repede şi corect .

Answer 1

$M=\left \{ x\:|\:x\:\in\:\mathbb{N} ,x=3n-4,n\:\in\:\mathbb{N},x<25\right \}$

$pt. \: n = 0 = > x = 3 \times 0 - 4 = - 4 \: \notin \: \mathbb{N}$

$pt. \: n = 1 = > x = 3 \times 1 - 4 = - 1 \: \notin \: \mathbb{N}$

$pt. \: n = 2 = > x = 3 \times 2 - 4 = 2 \: \in \: \mathbb{N},x<25$

$pt. \: n = 3 = > x = 3 \times 3 - 4 = 5 \: \in \: \mathbb{N},x<25$

$pt. \: n = 4 = > x = 3 \times 4 - 4 = 8\: \in \: \mathbb{N},x<25$

$pt. \: n = 5 = > x = 3 \times 5 - 4 = 11\: \in \: \mathbb{N},x<25$

$pt. \: n = 6 = > x = 3 \times 6 - 4 = 14 \: \in \: \mathbb{N},x<25$

$pt. \: n = 7 = > x = 3 \times 7 - 4 = 17 \: \in \: \mathbb{N},x<25$

$pt. \: n = 8 = > x = 3 \times 8 - 4 = 20\: \in \: \mathbb{N},x<25$

$pt. \: n = 9 = > x = 3 \times 9 - 4 = 23 \: \in \: \mathbb{N},x<25$

$= > x \: \in \: \left \{ 2,5,8,11,14,17,20,23 \right \}$

$= > M=\left \{ 2,5,8,11,14,17,20,23 \right \}$

Answer 2

M={x| x∈N, x=3n -4, n∈ N, x<25}

0≤x<25

0≤3n-4<25,   adunam 4

4≤3n<29

n ∈ {2,3,4,5,6,7,8,9}

x∈{2,5,8,11,14,17,20,23}

=> card M=8,   M are 8 elemente