示例：逻辑运算符

运算符 > 布尔运算符 > 示例：逻辑运算符

示例：逻辑运算符

可以简化其中包含逻辑运算符和比较运算符的表达式。对此类表达式进行简化，将返回更易于理解的优化结果。

逻辑 AND

• 对具有两个区间且这两个区间不相交的表达式进行求值。

• 使用关键字 simplify 对表达式求值。由于区间互不重叠，结果为 0 (false)。

• 对具有两个区间且这两个区间相交于一点的表达式进行求值。使用关键字 simplify 对表达式求值，将返回交点。

<region id="ID0EJRLR" 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>

• 对具有两个区间且其中一个区间包含在另一个区间中的表达式进行求值。使用关键字 simplify 对表达式求值，将返回最小区间。

<region id="ID0E4SLR" 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>

• 对具有两个区间且这两个区间在特定范围内相交的表达式进行求值。使用关键字 simplify 对表达式进行求值，将返回交集范围。

<region id="ID0ENULR" 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>

逻辑 OR

• 对具有两个区间且这两个区间与整个域重叠的表达式进行求值。使用关键字 simplify 对表达式进行求值，将返回域。

<region id="ID0EOWLR" 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>

• 对区间仅排除一个点的表达式进行求值。使用关键字 simplify 对表达式进行求值，将返回排除的点。

<region id="ID0ECYLR" 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>

• 对具有两个区间且其中一个区间包含在另一个区间中的表达式进行求值。使用关键字 simplify 对表达式进行求值，将返回最大区间。

<region id="ID0EWZLR" 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>