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Giải bài 4 trang 27 SGK Toán 10 tập 1 – Chân trời sáng tạo

Phát biểu lại định lí này sử dụng thuật ngữ “điều kiện cần và đủ”.

𓃲Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho định lí: “\(\forall x \in \mathbb{R},x \in \mathbb{Z}\) nếu và chỉ nếu \(x + 1 \in \mathbb{Z}\)”. Phát biểu lại định lí này sử dụng thuật ngữ “điều kiện cần và đủ”.

Phương pháp giải - Xem chi tiết

Mệnh đề trên có dạng “P nếu và chỉ nếu Q”, là một mệnh đề tương đương. Có thể phát biểu là: “P là điều kiện cần và đủ để có Q” (hoặc “Q là điều kiện cần và đủ để có P”)

Lời giải chi tiết

Mệnh đề trên có dạng “P nếu và chỉ nếu Q”, là một mệnh đề tương đương với P: “\(x \in \mathbb{Z}\)” và Q: “\(x + 1 \in \mathbb{Z}\)” (\(x \in \mathbb{R}\))Phát biểu: “\(\forall x \in \mathbb{R},x \in \mathbb{Z}\) là điều kiện cần và đủ để có \(x + 1 \in \mathbb{Z}\)”Hoặc “\(\forall x \in \mathbb{R},x + 1 \in \mathbb{Z}\) là điều kiện cần và đủ để có \(x \in \mathbb{Z}\)”

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