diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 0b8bddd4..49ca7d07 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -313715,7 +313715,8 @@
         ],
         "same": [],
         "related": [
-            "000017"
+            "000017",
+            "019806"
         ],
         "remark": "",
         "space": "4em",
@@ -509490,6 +509491,32 @@
         "space": "4em",
         "unrelated": []
     },
+    "019806": {
+        "id": "019806",
+        "content": "证明: $\\sqrt 3$是无理数.",
+        "objs": [],
+        "tags": [
+            "第一单元"
+        ],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "空中课堂必修第一册例题与习题-20230906修改",
+        "edit": [
+            "20220901\t王伟叶",
+            "20230906\t赵琍琍"
+        ],
+        "same": [],
+        "related": [
+            "000017",
+            "011778"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "020001": {
         "id": "020001",
         "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",