集合的运算
2020-06-08 00:54
本范例演示了集合的基本运算及其几何直观表示。通过GeoGebra的动态几何功能,利用点、线段等几何对象来可视化集合之间的关系,帮助用户更好地理解抽象的集合概念及其运算规律。
GeoGebra 画板及绘图内容加载中,请稍等……
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.580.0" app="classic" platform="w" id="17a4e9ca-f964-4525-9b94-ec7fc84ad7fd" xsi:noNamespaceSchemaLocation="https://ggb123.cn/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1339" height="557" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="1" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3" size="1339" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="325" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="493" window="100,100,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1339" height="557"/>
<coordSystem xZero="526.9925071326131" yZero="300.2633581465421" scale="22.489778026131592" yscale="22.489778026131724"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="2" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="1.850209397538824"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200" x="18" y="51" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<command name="PointIn">
<input a0="(x - a)^(2) + y^(2) = 25"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="5" y="8"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="5.957850707443066" y="2.8508389763661075" z="1"/>
<pointSize val="5"/>
<pointStyle val="4"/>
</element>
<expression label="D" exp="(a, 0)" type="point" />
<element type="point" label="D">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.850209397538824" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="4"/>
</element>
<command name="Length">
<input a0="Segment[D, E]"/>
<output a0="r"/>
</command>
<element type="numeric" label="r">
<value val="4.999999999999999"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<element type="numeric" label="r_1">
<value val="4.9"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="0" max="5" absoluteScreenLocation="true" width="200" x="16" y="98" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="1" type="0" playing="false"/>
</element>
<expression label="a_1" exp="a_1(x, y) = x^(2) / 100 + y^(2) / 64 ≤ 1"/>
<element type="functionNVar" label="a_1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-6" y="-37"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<caption val="U"/>
</element>
<expression label="c" exp="c(x, y) = (x + 5)^(2) + y^(2) ≤ 13"/>
<element type="functionNVar" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<lineStyle thickness="6" type="0" typeHidden="1"/>
<caption val="A"/>
</element>
<expression label="d" exp="d(x, y) = (x - a)^(2) + y^(2) ≤ r^(2)" />
<element type="functionNVar" label="d">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<caption val="B"/>
</element>
<expression label="e" exp="e(x, y) = c(x, y) ∧ d(x, y)" />
<element type="functionNVar" label="e">
<show object="true" label="false" ev="4"/>
<condition showObject="g"/>
<objColor r="219" g="97" b="20" alpha="0.75"/>
<layer val="0"/>
<labelMode val="3"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<expression label="f" exp="f(x, y) = c(x, y) ∨ d(x, y)" />
<element type="functionNVar" label="f">
<show object="false" label="false" ev="4"/>
<condition showObject="b"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<element type="boolean" label="g">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="35" y="130"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="A∩B"/>
</element>
<element type="boolean" label="b">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="35" y="178"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="A∪B"/>
</element>
<expression label="h" exp="h(x, y) = (x + 5)^(2) + y^(2) ≥ 13"/>
<element type="functionNVar" label="h">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<expression label="i" exp="i(x, y) = a_1(x, y) ∧ h(x, y)" />
<element type="functionNVar" label="i">
<show object="true" label="false"/>
<condition showObject="j"/>
<objColor r="101" g="87" b="210" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<element type="boolean" label="j">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="36" y="224"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="C_∪A"/>
</element>
<expression label="k" exp="k(x, y) = (x - a)^(2) + y^(2) ≥ r^(2) ∧ a_1(x, y)" />
<element type="functionNVar" label="k">
<show object="false" label="false" ev="4"/>
<condition showObject="l"/>
<objColor r="255" g="255" b="0" alpha="0.5699999928474426"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
</element>
<element type="boolean" label="l">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="36" y="267"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="C_∪B"/>
</element>
<expression label="m" exp="m(x, y) = i(x, y) ∧ k(x, y)" />
<element type="functionNVar" label="m">
<show object="false" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<expression label="n" exp="n(x, y) = i(x, y) ∨ k(x, y)" />
<element type="functionNVar" label="n">
<show object="false" label="true"/>
<objColor r="213" g="0" b="249" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<element type="boolean" label="o">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="36" y="307"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="C_∪(A∪B)=(C_UA)∩(C_UB)"/>
</element>
<expression label="p" exp="p(x, y) = i(x, y) ∨ k(x, y)" />
<element type="functionNVar" label="p">
<show object="true" label="true"/>
<condition showObject="q"/>
<objColor r="216" g="27" b="96" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
</element>
<element type="boolean" label="q">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="36" y="348"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="C_∪(A∩B)=(C_UA)∪(C_UB)"/>
</element>
<expression label="text1" exp=""集合的交集、并集、补集""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="12" style="0"/>
<absoluteScreenLocation x="311" y="15"/>
</element>
<command name="Point">
<input a0="x^(2) / 100 + y^(2) / 64 = 1"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-4.958108039062589" y="6.947444522319633" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Text">
<input a0=""U"" a1="A"/>
<output a0="text2"/>
</command>
<element type="text" label="text2">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2" size="12" style="1"/>
<startPoint x="-4.958108039062589" y="6.947444522319633" z="1"/>
</element>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-7.059981631877375" y="2.943717718175926" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="(x - a)^(2) + y^(2) = r_1^(2)"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.7029402564839415" y="3.9839586652502126" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Text">
<input a0=""A"" a1="B + (-0.5, -0.5)"/>
<output a0="text3"/>
</command>
<element type="text" label="text3">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2" size="12" style="1"/>
<startPoint x="-7.559981631877375" y="2.443717718175926" z="1"/>
</element>
<command name="Point">
<input a0="(x - a)^(2) + y^(2) = r^(2)"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.3364455624616083" y="4.774002729584013" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Text">
<input a0=""B"" a1="F"/>
<output a0="text4"/>
</command>
<element type="text" label="text4">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2" size="12" style="1"/>
<startPoint x="3.3364455624616083" y="4.774002729584013" z="1"/>
</element>
<element type="point" label="G">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-13" y="55"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-20.965721855954875" y="10.790944777793124" z="1"/>
<pointSize val="5"/>
<pointStyle val="4"/>
<caption val="$\large 注:拖动点可以改变B的大小和位置$"/>
</element>
</construction>
</geogebra>