Cho các tập hợp sau:
A = {x ∈ ℤ | 2 < x – 1 < 4};
B = {x ∈ ℕ | 3 < 2x – 3 < 5};
C = {x ∈ ℕ | x < 5}.
Trong các tập hợp trên, có bao nhiêu tập hợp là tập hợp rỗng?
Cho các tập hợp sau:
A = {x ∈ ℤ | 2 < x – 1 < 4};
B = {x ∈ ℕ | 3 < 2x – 3 < 5};
C = {x ∈ ℕ | x < 5}.
Trong các tập hợp trên, có bao nhiêu tập hợp là tập hợp rỗng?Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Ta xét từng tập hợp:
- A = {x ∈ Z | 2 < x - 1 < 4}. 2 < x - 1 < 4 <=> 3 < x < 5. Vì x ∈ Z, nên x = 4. Vậy A = {4} (không phải tập rỗng).
- B = {x ∈ R | 3 < 2x - 3 < 5}. 3 < 2x - 3 < 5 <=> 6 < 2x < 8 <=> 3 < x < 4. Vì $x \in \mathbb{N}$ nên không có giá trị nào của $x$ thỏa mãn. Vậy B = Ø.
- C = {x ∈ R | x < 5}. Vậy C = (-∞; 5) (không phải tập rỗng).
Vậy có 1 tập hợp rỗng trong các tập hợp đã cho.
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