154 lines
7.4 KiB
Plaintext
154 lines
7.4 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"000436 True\n",
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"007709 True\n",
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"002746 True\n",
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"000003 True\n",
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"000986 True\n",
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"000977 True\n",
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"020079 True\n",
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"002734 True\n",
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"000978 True\n",
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"020089 True\n",
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"002733 True\n",
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"000009 True\n",
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"020081 True\n",
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"004875 True\n",
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"004854 True\n",
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"004847 True\n",
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"004894 True\n",
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"004873 False\n",
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"已知$\\triangle ABC$的三边为$a,b,c$求证: 关于$x$的方程$x^2+2ax+b^2=0$与$x^2+2cx-b^2=0$有公共根的一个充要条件是$A=90^\\circ$.\n",
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"已知$\\triangle ABC$的三边为$a,b,c$求证: 关于$x$的方程$x^2+2ax+b^2=0$与$x^2+2cx-b^2=0$有公共根的充要条件是$A=90^\\circ$.\n",
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"002747 False\n",
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"已知$m$是实常数. 命题甲: 关于$x$的方程$x^2+x+m=0$有两个相异的负根; 命题乙: 关于$x$的方程$4x^2+x+m=0$无实根, 若这两个命题有且只有一个是真命题, 求实数$m$的取值范围.\n",
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"*\n",
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"已知$m$是实常数. 命题甲: 关于$x$的方程$x^2+x+m=0$有两个相异的负根; 命题乙: 关于$x$的方程$4x^2+x+m=0$无实根, 若这两个命题有且只有一个是真命题, 求实数$m$的取值范围.\n",
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"000018 True\n",
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"003708 True\n",
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"000431 True\n",
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"002737 True\n",
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"004282 True\n",
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"004876 True\n",
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"004878 False\n",
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"$a,b,c$三个数不全为零的一个充要条件是\\bracket{20}.\n",
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"\\twoch{$a,b,c$三个数都不是零}{$a,b,c$三个数中至多有一个是零}{$a,b,c$三个数中只有一个是零}{$a,b,c$三个数中至少有一个不是零}\n",
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"$a,b,c$三个数不全为零的充要条件是\\bracket{20}.\n",
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"\\twoch{$a,b,c$三个数都不是零}{$a,b,c$三个数中至多有一个是零}{$a,b,c$三个数中只有一个是零}{$a,b,c$三个数中至少有一个不是零}\n",
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"007736 True\n",
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"010030 False\n",
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"判断下列语句是否为命题:\\\\\n",
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"(1) 有的正方形是三角形;\\\\\n",
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"(2) 任意一个三角形的内角和都为$180^\\circ$;\\\\\n",
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"(3) $1$是自然数吗?\\\\\n",
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"(4) $3>\\pi$;\\\\\n",
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"(5) $2\\in (0, 5)$, 且$2\\in \\mathbf{Z}$.\n",
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"判断下列语句是否为命题:\\\\\n",
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"(1) 有的正方形是三角形;\\blank{50}; (2) 任意一个三角形的内角和都为$180^\\circ$;\\blank{50}; (3) $1$是自然数吗?\\blank{50}; (4) $3>\\pi$;\\blank{50}; (5) $2\\in (0, 5)$, 且$2\\in \\mathbf{Z}$;\\blank{50}.\n",
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"020072 False\n",
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"在下列各题中, 用符号``$\\Rightarrow$''``$\\Leftarrow$''``$\\Leftrightarrow$''把$\\alpha$和$\\beta$联系起来:\\\\\n",
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"(1) $\\alpha:a=0$, $\\beta:ab=0$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(2) $\\alpha:x^2=4$, $\\beta:x=2$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(3) $\\alpha:$实数$x$适合$x^2-5x+6=0$, $\\beta:x=2$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(4) $\\alpha:\\sqrt {x^2}=x$, $\\beta:x>0$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(5) $\\alpha:$实数$x$适合$\\dfrac{x-3}{x+1}=-1$, $\\beta:x=1$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(6) $\\alpha:k$除以$4$余$1$, $\\beta:k$除以$2$余$1$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(7) $\\alpha: \\{2\\}\\subset B\\subseteq \\{2, 3, 5\\}$, $\\beta:B=\\{2, 5\\}$; $\\alpha$\\blank{20}$\\beta$.\n",
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"在下列各题中, 用符号``$\\Rightarrow$''``$\\Leftarrow$''``$\\Leftrightarrow$''把$\\alpha$和$\\beta$联系起来:\\\\\n",
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"(1) $\\alpha:a=0$, $\\beta:ab=0$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(2) $\\alpha:x^2=4$, $\\beta:x=2$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(3) $\\alpha:$实数$x$适合$x^2-5x+6=0$, $\\beta:x=2$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(4) $\\alpha:\\sqrt {x^2}=x$, $\\beta:x>0$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(5) $\\alpha:$实数$x$适合$\\dfrac{x-3}{x+1}=-1$, $\\beta:x=1$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(6) $\\alpha:k$除以$4$余$1$, $\\beta:k$除以$2$余$1$; $\\alpha$\\blank{20}$\\beta$;\\\\\n",
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"(7)$\\alpha: \\{2\\}\\subset B\\subseteq \\{2, 3, 5\\}$, $\\beta:B=\\{2, 5\\}$; $\\alpha$\\blank{20}$\\beta$.\n",
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"002740 True\n",
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"004886 True\n",
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"007719 False\n",
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"判断下列命题的真假, 并在相应的横线上填入``真命题''或``假命题''.\\\\\n",
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"(1) 若$A\\cap B\\ne \\varnothing$, $B\\subset C$, 则$A\\cap C\\ne \\varnothing$\\blank{20};\\\\\n",
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"(2) 方程$(a+1)x+b=0$($a$、$b\\in \\mathbf{R}$)的解为$x=-\\dfrac b{a+1}$\\blank{20};\\\\\n",
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"(3) 若命题$\\alpha$、$\\beta$、$\\gamma$满足$\\alpha \\Rightarrow \\beta$, $\\beta \\Rightarrow \\gamma$, $\\gamma \\Rightarrow \\alpha$, 则$\\alpha \\Leftrightarrow \\gamma$\\blank{20}.\n",
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"判断下列命题的真假, 并在相应的横线上填入``真命题''或``假命题''.\\\\\n",
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"(1) 若$A\\cap B\\ne \\varnothing$, $B\\subset C$, 则$A\\cap C\\ne \\varnothing$\\blank{20};\\\\\n",
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"(2) 方程$(a+1)x+b=0$($a$、$b\\in \\mathbf{R}$)的解为$x=-\\dfrac b{a+1}$\\blank{20};\\\\\n",
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"(3)若命题$\\alpha$、$\\beta$、$\\gamma$满足$\\alpha \\Rightarrow \\beta$, $\\beta \\Rightarrow \\gamma$, $\\gamma \\Rightarrow \\alpha$, 则$\\alpha \\Leftrightarrow \\gamma$\\blank{20}.\n",
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"002731 True\n",
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"000981 True\n",
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"004864 False\n",
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"已知命题$p$: 如果$a^2+2ab+b^2+a+b-2\\ne 0$, 那么$a+b\\ne 1$, 求证: 命题$p$是真命题.\n",
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"已知命题$p$: 如果$a^2+2ab+b^2+a+b-2\\ne 0$, 那么$a+b\\ne 1$, 求证: 命题$p$是真命题.\n",
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"\\end{enumerate}\n"
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]
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}
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],
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"source": [
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"import os,re,json\n",
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"\n",
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"#读取题库json文件并转化为字典\n",
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"with open(r\"../题库0.3/Problems.json\",\"r\",encoding = \"utf8\") as f:\n",
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" database = f.read()\n",
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"pro_dict = json.loads(database)\n",
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"with open(r\"C:\\Users\\weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\02_常用逻辑用语.tex\",\"r\",encoding = \"u8\") as f:\n",
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" data = f.read()\n",
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"problems_raw = re.findall(r\"\\(([\\d]{6})\\)\\}([\\s\\S]*?)\\n\\n\",data)\n",
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"problems_list = []\n",
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"for p in problems_raw:\n",
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" if \"vspace\" in p[1]:\n",
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" problems_list.append((p[0],p[1][:p[1].index(r\"\\vspace\")]))\n",
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" else:\n",
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" problems_list.append(p)\n",
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" \n",
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"for p in problems_list:\n",
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" print(p[0],pro_dict[p[0]][\"content\"].strip() == p[1].strip())\n",
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" if not pro_dict[p[0]][\"content\"].strip() == p[1].strip():\n",
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" print(pro_dict[p[0]][\"content\"].strip())\n",
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" print(p[1].strip())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"orig_nbformat": 4,
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"vscode": {
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"nbformat": 4,
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"nbformat_minor": 2
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}
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