Question

Scrieti elementele multimilor:
A={x/x€N,x=2k+1,k€N,k≤3}
B={x/x€N,x=2la puterea k, k€N, k<4}
C={x/x€N,2la puterea x≤32}
D={x/€N,x la puterea 4,≤64}
Urgent va rog!!!!

Answer 1

Răspuns:

A = {1; 3; 5; 7}

B = {1; 2; 4; 8}

C = {0; 1; 2; 3; 4; 5}

D = {0; 1; 2}

Explicație:

A = {x | x ∈ N, x = 2k + 1, k ∈ N, k ≤ 3}

k ∈ {0, 1, 2, 3}

⇒ x = 2k + 1 ∈ {2·0+1; 2·1+1; 2·2+1; 2·3+1}

x ∈ {0+1; 2+1; 4+1; 6+1}

A = {1; 3; 5; 7}

B = {x | x ∈ N, x = $2^{k}$, k ∈ N, k < 4}

k ∈ {0, 1, 2, 3}

⇒ x = $2^{k}$ ∈ {2⁰; 2¹; 2²; 2³}

B = {1; 2; 4; 8}

C = {x | x ∈ N, 2ˣ ≤ 32}

2⁵ = 32  ⇒  x ≤ 5

C = {0; 1; 2; 3; 4; 5}

D = {x | x ∈ N, x⁴ ≤ 64}

2⁴ = 16 < 64

3⁴ = 81 > 64

⇒ x ≤ 2

D = {0; 1; 2}