Operations on Sets
2020-06-08 00:54
This applet demonstrates the basic operations on sets and their geometric representations. Using GeoGebra's dynamic geometry features, it visualizes the relationships between sets through geometric objects like points and segments, helping users better understand abstract set concepts and operation rules.
Loading the GeoGebra board and drawing, please wait…
<?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>