範例：邏輯運算子

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範例：邏輯運算子

您可以簡化具有邏輯運算子和比較運算子的運算式。簡化這類運算式會傳回修飾後的結果，較容易理解。

邏輯 AND

• 計算具有兩個區間的運算式，且兩個區間沒有交集。

• 計算使用了關鍵字 simplify 的運算式。由於區間未重疊，因此結果為 0 (false)。

• 計算具有兩個區間的運算式，且兩個區間交集於一點。以關鍵字 simplify 計算會傳回交點。

<region id="ID0ENRLR" actualWidth="288.79800093889236" actualHeight="39.2" top="268.80000000000007" left="57.600000000000009" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="10">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <and />
        <apply>
          <greaterOrEqual />
          <apply>
            <minus />
            <apply>
              <nthRoot />
              <placeholder />
              <id xml:space="preserve">a</id>
            </apply>
            <real>2</real>
          </apply>
          <real>0</real>
        </apply>
        <apply>
          <greaterOrEqual />
          <apply>
            <plus />
            <apply>
              <neg />
              <apply>
                <nthRoot />
                <placeholder />
                <id xml:space="preserve">a</id>
              </apply>
            </apply>
            <real>2</real>
          </apply>
          <real>0</real>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">simplify</id>
      </command>
      <symResult>
        <apply>
          <equal />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve" labels="VARIABLE">a</id>
          </apply>
          <real>2</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

• 計算具有兩個區間的運算式，且其中一個區間位於另一個區間內。以關鍵字 simplify 計算會傳回最小區間。

<region id="ID0EBTLR" actualWidth="277.59800093889237" actualHeight="39.2" top="384.00000000000006" left="57.600000000000009" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="11">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <and />
        <apply>
          <greaterOrEqual />
          <apply>
            <minus />
            <apply>
              <nthRoot />
              <placeholder />
              <id xml:space="preserve">a</id>
            </apply>
            <real>2</real>
          </apply>
          <real>0</real>
        </apply>
        <apply>
          <greaterOrEqual />
          <apply>
            <minus />
            <apply>
              <nthRoot />
              <placeholder />
              <id xml:space="preserve">a</id>
            </apply>
            <real>1</real>
          </apply>
          <real>0</real>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">simplify</id>
      </command>
      <symResult>
        <apply>
          <greaterOrEqual />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve" labels="VARIABLE">a</id>
          </apply>
          <real>2</real>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 計算具有兩個區間的運算式，且兩個區間交集於特定值域。使用關鍵字 simplify 執行計算會傳回交集值域。

<region id="ID0ERULR" actualWidth="332.57800093889239" actualHeight="39.2" top="480.00000000000006" left="76.800000000000011" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="12">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <and />
        <apply>
          <greaterOrEqual />
          <apply>
            <minus />
            <apply>
              <neg />
              <apply>
                <nthRoot />
                <placeholder />
                <id xml:space="preserve">a</id>
              </apply>
            </apply>
            <real>1</real>
          </apply>
          <real>0</real>
        </apply>
        <apply>
          <greaterOrEqual />
          <apply>
            <plus />
            <apply>
              <nthRoot />
              <placeholder />
              <id xml:space="preserve">a</id>
            </apply>
            <real>2</real>
          </apply>
          <real>0</real>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">simplify</id>
      </command>
      <symResult>
        <apply>
          <lessOrEqual />
          <apply>
            <lessOrEqual />
            <real>-2</real>
            <apply>
              <nthRoot />
              <placeholder />
              <id xml:space="preserve" labels="VARIABLE">a</id>
            </apply>
          </apply>
          <real>-1</real>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

邏輯 OR

• 計算具有兩個區間的運算式，且兩個區間重疊整個值域。以關鍵字 simplify 計算會傳回值域。

<region id="ID0ESWLR" actualWidth="235.0413342722257" actualHeight="39.2" top="921.60000000000014" left="96.000000000000014" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="13">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <or />
        <apply>
          <greaterOrEqual />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve">a</id>
          </apply>
          <real>2</real>
        </apply>
        <apply>
          <greaterOrEqual />
          <real>2</real>
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve">a</id>
          </apply>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">simplify</id>
      </command>
      <symResult>
        <apply>
          <elementOf />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve" labels="VARIABLE">a</id>
          </apply>
          <id xml:space="preserve" labels="CONSTANT">ℝ</id>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

• 計算具有兩個區間的運算式，且兩個區間只排除一點。以關鍵字 simplify 計算會傳回排除的點。

<region id="ID0EGYLR" actualWidth="230.13800093889239" actualHeight="39.2" top="1075.2000000000003" left="96.000000000000014" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="14">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <or />
        <apply>
          <lessThan />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve">a</id>
          </apply>
          <real>2</real>
        </apply>
        <apply>
          <lessThan />
          <real>2</real>
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve">a</id>
          </apply>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">simplify</id>
      </command>
      <symResult>
        <apply>
          <notEqual />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve" labels="VARIABLE">a</id>
          </apply>
          <real>2</real>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 計算具有兩個區間的運算式，且其中一個區間包含於另一個區間內。以關鍵字 simplify 計算會傳回最大區間。

<region id="ID0E1ZLR" actualWidth="253.63800093889239" actualHeight="39.2" top="1228.8000000000002" left="96.000000000000014" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="15">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <or />
        <apply>
          <greaterOrEqual />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve">a</id>
          </apply>
          <real>2</real>
        </apply>
        <apply>
          <greaterThan />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve">a</id>
          </apply>
          <real>-2</real>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">simplify</id>
      </command>
      <symResult>
        <apply>
          <greaterThan />
          <apply>
            <nthRoot />
            <placeholder />
            <id xml:space="preserve" labels="VARIABLE">a</id>
          </apply>
          <real>-2</real>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

相關主題

邏輯運算子

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