Question

27. Se consideră mulţimile 4-(xe N' 1x54), B-(xe Nix-20-1, a€ 4) gi C-[ye N[y-2x+1, BUC), BBC. (BAQUA, xe Bj, Determinati multimile A, B, C.UBU(BSC), SUBSC
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Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

A = {x ∈ N* | x ≤ 4}

=> A = {1; 2; 3; 4}

B = {x ∈ N | x = 2a - 1, a ∈ A}

a = 1 => x = 2×1 - 1 = 2 - 1 = 1

a = 2 => x = 2×2 - 1 = 4 - 1 = 3

a = 3 => x = 2×3 - 1 = 6 - 1 = 5

a = 4 => x = 2×4 - 1 = 8 - 1 = 7

=> B = {1; 3; 5; 7}

C = {y ∈ N | y = 2x + 1, x ∈ B}

x = 1 => y = 2×1 + 1 = 2 + 1 = 3

x = 3 => y = 2×3 + 1 = 6 + 1 = 7

x = 5 => y = 2×5 + 1 = 10 + 1 = 11

x = 7 => y = 2×7 + 1 = 14 + 1 = 15

=> C = {3; 7; 11; 15}

(A∩B) ∪ (B∩C) = {1;3} ∪ {3;7} = {1; 3; 7}

(A - B) ∪ (B - C) = {2;4} ∪ {1;5} = {1; 2; 4; 5}

(A - B) ∩ (B∩C) = {2;4} ∩ {3;7} = {Ø}

(B∩C) ∪ A = {3;7} ∪ {1;2;3;4} = {1; 2; 3; 4; 7}

(A∪B) ∩ C = {1;2;3;4;5;7} ∩ {3;7;11;15} = {3; 7}