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
- $A = \{x \in \mathbb{Z} | 2 < x – 1 < 4\}$
$2 < x - 1 < 4 \Leftrightarrow 3 < x < 5$. Vì $x \in \mathbb{Z}$ nên $x = 4$. Vậy $A = \{4\}$ (A khác rỗng) - $B = \{x \in \mathbb{R} | 3 < 2x – 3 < 5\}$
$3 < 2x - 3 < 5 \Leftrightarrow 6 < 2x < 8 \Leftrightarrow 3 < x < 4$. Vậy $B = (3; 4)$ (B khác rỗng) - $C = \{x \in \mathbb{R} | x < 5\}$. Vậy $C = (- \infty; 5)$ (C khác rỗng)
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