From 9099727209c853a6ed10c431ac53646cc117c9ed Mon Sep 17 00:00:00 2001
From: wangweiye7840 <kj_wangweiye@126.com>
Date: Mon, 8 Jan 2024 10:05:19 +0800
Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A526=E5=B1=8A=E5=AF=92=E5=81=87?=
 =?UTF-8?q?=E4=BD=9C=E4=B8=9A1=E5=B9=B6=E5=BB=BA=E7=AB=8Brelated?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 题库0.3/Problems.json | 438 ++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 424 insertions(+), 14 deletions(-)

diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 861c8270..a72cac5d 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -219013,7 +219013,9 @@
             "20220726\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023378"
+        ],
         "remark": "",
         "space": "3em",
         "unrelated": []
@@ -326277,7 +326279,8 @@
         ],
         "same": [],
         "related": [
-            "009442"
+            "009442",
+            "023382"
         ],
         "remark": "",
         "space": "4em",
@@ -332592,7 +332595,9 @@
             "20221110\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023375"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -355391,7 +355396,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023385"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -355528,7 +355535,9 @@
             "20230118\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023380"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -390796,7 +390805,9 @@
             "20230131\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023373"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -425909,7 +425920,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023376"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -532278,7 +532291,8 @@
         ],
         "same": [],
         "related": [
-            "007740"
+            "007740",
+            "023381"
         ],
         "remark": "",
         "space": "4em",
@@ -594840,7 +594854,9 @@
             "20230905\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023371"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -595477,7 +595493,9 @@
             "20230905\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023381"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -595972,7 +595990,9 @@
             "20230905\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023381"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -607339,7 +607359,9 @@
             "20230905\t朱敏慧"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023375"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -608334,7 +608356,9 @@
             "20231109\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023375"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -625036,6 +625060,390 @@
         "space": "4em",
         "unrelated": []
     },
+    "023371": {
+        "id": "023371",
+        "content": "已知 $A=\\{x |-3<x<2\\}$, $B=\\{x | x-a \\leq 0\\}$, 若 $A \\cap B=\\varnothing$, 则 $a$ 的取值范围是\\blank{50}; 若 $A \\subset B$, 则 $a$ 的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "022158"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023372": {
+        "id": "023372",
+        "content": "已知 $m$ 是实常数, 设集合 $A=\\{(x, y) | y=1-3 x\\}$, $B=\\{(x, y) | y=(1-2 m^2) x+5\\}$, 若 $A \\cap B=\\varnothing$, 则实数 $m$ 的值的集合是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023373": {
+        "id": "023373",
+        "content": "已知集合 $P=\\{y | y=x^2, x \\in \\mathbf{R}\\}$, $Q=\\{y | y=-2 x^2+3, x \\in \\mathbf{R}\\}$, 则 $P \\cap Q=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "014117"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023374": {
+        "id": "023374",
+        "content": "已知集合 $A=\\{(x, y) | x^2+y^2\\leq 3, x \\in \\mathbf{Z}, y \\in \\mathbf{Z}\\}$, 则 $A$ 中元素的个数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023375": {
+        "id": "023375",
+        "content": "语句``$a>0$ 或 $b \\leq 0$''的否定形式为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "022698",
+            "022663",
+            "012035"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023376": {
+        "id": "023376",
+        "content": "语句``对任意 $x \\in A$, 都有 $x \\in B$''的否定形式为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "015399"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023377": {
+        "id": "023377",
+        "content": "(1)已知 $x$、$y \\in \\mathbf{R}$, $``x y>0$, $x+y>0$''是``$x>0$, $y>0''$ 的\\blank{50}条件;\\\\\n(2) 已知 $x$、$y \\in \\mathbf{R}$, $``x y>1$, $x+y>2$''是``$x>1$, $y>1$''的\\blank{50}条件;\\\\\n(3) 已知 $x$、$y \\in \\mathbf{R}$, $``(x-1)^2+(y-2)^2=0$''是``$(x-1)(y-2)=0$''的\\blank{50}条件.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023378": {
+        "id": "023378",
+        "content": "知 $a$ 是实常数, 若 $P=\\{x | x^2+x-6=0\\}$, $S=\\{x | a x+1=0\\}$, 写出使 $S \\subseteq P$ 成立的一个充分非必要条件: \\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "007692"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023379": {
+        "id": "023379",
+        "content": "若函数 $y=f(x)$、$y=g(x)$ 的定义域都是 $\\mathbf{R}$, 则``$f(x)>g(x)$ 对一切 $x \\in \\mathbf{R}$ 成立''的充要条件是\\bracket{20}.\n\\twoch{存在 $x \\in \\mathbf{R}$, 使得 $f(x)>g(x)$}{有无穷多个 $x \\in \\mathbf{R}$, 使得 $f(x)>g(x)$}{不存在 $x \\in \\mathbf{R}$, 使得 $f(x) \\leq g(x)$}{任取 $x \\in \\mathbf{R}$, 都有 $f(x)>g(x)+1$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023380": {
+        "id": "023380",
+        "content": "设全集 $U=\\mathbf{R}$, $A, B$ 是两个集合, 则``存在集合 $C$, 使得 $A \\subseteq C$ 且 $B \\subseteq \\overline{C}$''是``$A \\cap B=\\varnothing$''的\\blank{50}条件.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "012791"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023381": {
+        "id": "023381",
+        "content": "已知陈述句 $\\alpha:-1<x<4$, 陈述句 $\\beta:-2<x<a+1$,且 $\\alpha \\Rightarrow \\beta$, 则实数 $a$ 的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020074",
+            "022186",
+            "022206"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023382": {
+        "id": "023382",
+        "content": "设 $n \\in \\mathbf{N}$, 若 $n^2$ 能被 $3$ 整除, 求证: $n$ 也能被 $3$ 整除.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "011776"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023383": {
+        "id": "023383",
+        "content": "已知集合 $A=\\{x | x^2-3 x+2=0\\}$, $B=\\{x | x^2-a x+a-1=0\\}$, $C=\\{x | x^2-b x+2=0\\}$, 若 $B \\subset A$, $C \\subseteq A$, 求实数 $a+b$ 的最大值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023384": {
+        "id": "023384",
+        "content": "``$a>0$ 且 $b>0$''是``对于任意 $x \\in[-1,1]$, $a x+b>0$ 成立''的\\blank{50}条件.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023385": {
+        "id": "023385",
+        "content": "设 $A$、$B$ 是非空集合, 定义 $A \\triangle B=\\{x | x \\in A \\cup B, x \\notin A \\cap B\\}$, 已知 $A=\\{x |$ 存在 $y \\in \\mathbf{R}$, 使得 $y=\\sqrt{2 x-x^2}\\}$, $B=\\{y | y=\\dfrac{2^x}{2^x-1}, x>0\\}$, 则 $A \\triangle B$ 等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "012786"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023386": {
+        "id": "023386",
+        "content": "已知 $c>0$, 设 $P$:  函数 $y=c^x$ 在 $\\mathbf{R}$ 上是减函数; $Q$ : 不等式 $x+|x-2 c|>1$ 的解集为 $\\mathbf{R}$. 如果命题 $P$ 和 $Q$ 有且仅有一个正确, 求 $c$ 的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "040285"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023387": {
+        "id": "023387",
+        "content": "设 $A=\\{(x, y) | y=x^2+3\\}$, $B=\\{(x, y) | y=2 x+m, 0 \\leq x \\leq 2\\}$. 若 $A \\cap B \\neq \\varnothing$, 则实数 $m$ 的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023388": {
+        "id": "023388",
+        "content": "设 $a$ 是非零的实常数, $f(x)=x^2+a|x-m+1|+1$ 是偶函数.\\\\\n(1) 求实数 $m$ 的值.\\\\\n(2) 问:``$a<-2$''是``函数 $f(x)$ 在区间 $(-2,0)$ 上存在两个零点''的什么条件(充分非必要条件、必要非充分条件、充要条件、既非充分也非必要条件) ? 并证明你的结论.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "26届寒假作业补充题目",
+        "edit": [
+            "20240108\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
@@ -686393,7 +686801,9 @@
             "20230324\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023386"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []