Salut! ♡
❀ Rezolvare
a) A = { x ∈ ℕ | 10 ≤ x < 15 } ➺ A = { 10, 11, 12, 13, 14 }
B = { x ∈ ℕ | 7 ≤ x ≤ 14 } ➺ B = { 7, 8, 9, 10, 11, 12, 13, 14 } ➺ A ⊂ B
b) A = { x ∈ ℕ | x divizor propriu al lui 18 } ➺ A = { 2, 3, 6, 9 }
B = { x ∈ ℕ | 54 ⋮ x } ➺ B = { 1, 2, 3, 6, 9, 18, 27, 54 } ➺ A ⊂ B
c) A = { 2⁰, 2¹, 2², 2³ } ➺ A = { 1, 2, 4, 8 }
B = { x ∈ ℕ | x | 8 } ➺ B = { 0, 1, 2, 4, 8 } ➺ A ⊂ B
d) A = { x ∈ ℤ | | x + 3 | < 5 } ➺ A = { - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1 }
- 5 < x + 3 < 5 | - 3
- 8 < x < 2
B = { x ∈ ℤ | | x | ≤ 7 } ➺ B = { - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6, 7 } ➺ A ⊂ B
- 7 ≤ x ≤ 7
e) A = { x ∈ ℕ | 4x + 11 > 67 } ➺ A = { 14, 15, 16, ..., ∞ }
4x + 11 > 67 | - 11
4x > 56 | : 4
x > 14
B = { x ∈ ℕ | 7x - 5 ≥ 72 } ➺ B = { 11, 12, 13, 14, 15, 16, ..., ∞ } ➺ A ⊂ B
7x - 5 ≥ 72 | + 5
7x ≥ 77 | : 7
x ≥ 11
f) A = { x ∈ ℕ | ( x² - 3 ) | 22 } ➺ A = { 2, 5 }
x² - 3 = { 0, 1, 2, 11, 22 } | + 3
x² = { 3, 4, 5, 14, 25 } ➺ x = { 2, 5 }
B = { x ∈ ℤ | | x | ≤ 5 } ➺ B = { - 5, - 4, - 3, ..., 2, 3, 4, 5 } ➺A ⊂ B
- 5 ≤ x ≤ 5
