運算子
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布林運算子
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範例：布林運算子
範例：布林運算子
計算布林運算式
透過插入布林運算式，再跟著計算運算子，計算布林運算式。
<region id="ID0EZIOR" top="120" left="48" xml:lang="zh_TW" height="21.2" width="57.6816666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <equal xml:lang="zh_TW" /> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">2</real> </apply> <result xml:lang="zh_TW"> <real xml:lang="zh_TW">0</real> </result> </eval> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0ELJOR" top="144" left="48" xml:lang="zh_TW" height="21.2" width="56.745" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <lessThan xml:lang="zh_TW" /> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">2</real> </apply> <result xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> </result> </eval> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
布林等於運算子與計算運算子不同。計算布林運算式時，1 表示 "true"，0 表示 "false"。
邏輯運算子
定義兩個向量。
<region id="ID0EULOR" top="360" left="48" xml:lang="zh_TW" height="64.331" width="47.6866666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">P</id> <matrix rows="4" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> </matrix> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EHMOR" top="360" left="192" xml:lang="zh_TW" height="64.331" width="48.81" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">Q</id> <matrix rows="4" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> </matrix> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
使用向量化運算子逐項數計算下列布林運算式：
NOT - 否定
<region id="ID0ENOOR" top="504" left="120" xml:lang="zh_TW" height="64.331" width="70.0416666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <vectorize xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <not xml:lang="zh_TW" /> <id xml:lang="zh_TW">P</id> </apply> </parens> </apply> <result xml:lang="zh_TW"> <matrix rows="4" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> </matrix> </result> </eval> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
AND - 結合
<region id="ID0ERPOR" top="576" left="120" xml:lang="zh_TW" height="64.331" width="80.4583333333333" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <vectorize xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <and xml:lang="zh_TW" /> <id xml:lang="zh_TW">P</id> <id xml:lang="zh_TW">Q</id> </apply> </parens> </apply> <result xml:lang="zh_TW"> <matrix rows="4" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> </matrix> </result> </eval> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
OR - 分離
<region id="ID0EVQOR" top="648" left="120" xml:lang="zh_TW" height="64.331" width="80.4583333333333" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <vectorize xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <or xml:lang="zh_TW" /> <id xml:lang="zh_TW">P</id> <id xml:lang="zh_TW">Q</id> </apply> </parens> </apply> <result xml:lang="zh_TW"> <matrix rows="4" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> </matrix> </result> </eval> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
XOR - 互斥
<region id="ID0EXROR" top="720" left="120" xml:lang="zh_TW" height="64.331" width="82.6583333333333" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <vectorize xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <xor xml:lang="zh_TW" /> <id xml:lang="zh_TW">P</id> <id xml:lang="zh_TW">Q</id> </apply> </parens> </apply> <result xml:lang="zh_TW"> <matrix rows="4" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> </matrix> </result> </eval> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
邏輯等價
您可以顯示 P ⋁ (Q ∧ R) 與 (P ⋁ Q) ∧ (P ⋁ R) 邏輯相等。
<region id="ID0EDUOR" top="960" left="48" xml:lang="zh_TW" height="120.926" width="47.6866666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">P</id> <matrix rows="8" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> </matrix> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EWUOR" top="960" left="120" xml:lang="zh_TW" height="120.926" width="48.81" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">Q</id> <matrix rows="8" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">0</real> </matrix> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EJVOR" top="960" left="192" xml:lang="zh_TW" height="120.926" width="48.38" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">R</id> <matrix rows="8" cols="1" xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> <real xml:lang="zh_TW">1</real> <real xml:lang="zh_TW">0</real> </matrix> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E2VOR" top="1056" left="48" xml:lang="zh_TW" height="25.2" width="92.56" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">A</id> <apply xml:lang="zh_TW"> <vectorize xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <or xml:lang="zh_TW" /> <id xml:lang="zh_TW">P</id> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <and xml:lang="zh_TW" /> <id xml:lang="zh_TW">Q</id> <id xml:lang="zh_TW">R</id> </apply> </parens> </apply> </parens> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0ENWOR" top="1056" left="192" xml:lang="zh_TW" height="25.2" width="119.55" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id xml:lang="zh_TW" label="None">B</id> <apply xml:lang="zh_TW"> <vectorize xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <and xml:lang="zh_TW" /> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <or xml:lang="zh_TW" /> <id xml:lang="zh_TW">P</id> <id xml:lang="zh_TW">Q</id> </apply> </parens> <parens xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <or xml:lang="zh_TW" /> <id xml:lang="zh_TW">P</id> <id xml:lang="zh_TW">R</id> </apply> </parens> </apply> </parens> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0E6WOR" top="1080" left="48" xml:lang="zh_TW" height="21.2" width="62.3583333333333" xmlns="http://schemas.mathsoft.com/worksheet50"> <math xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <equal xml:lang="zh_TW" /> <id xml:lang="zh_TW">A</id> <id xml:lang="zh_TW">B</id> </apply> <result xml:lang="zh_TW"> <real xml:lang="zh_TW">1</real> </result> </eval> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" xml:lang="zh_TW" /> </resultFormat> </math> </region>
複製運算式
