2.3 声明

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  如果- 然后声明

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  Conditional Statements
  ::有条件声明

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  A conditional statement (also called an if-then statement ) is a statement with a hypothesis followed by a conclusion . The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement. The conclusion is the result of a hypothesis.
  ::有条件声明(也称为 " 如果当时的声明 " )是附有假设的声明,然后是结论,假设是有条件声明的第一个部分或 " 如果 " 部分,结论是有条件声明的第二个部分或 " 当时 " 部分,结论是假设的结果。

  

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  If-then statements might not always be written in the “if-then” form. Here are some examples of conditional statements:
  ::如果当时的声明不一定总是以“如果当时”的形式写成。

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  • Statement 1: If you work overtime, then you’ll be paid time-and-a-half.
    ::报表1:如果加班工作,将领取半薪。
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  • Statement 2: I’ll wash the car if the weather is nice.
    ::声明2:如果天气好,我会洗车。
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  • Statement 3: If 2 divides evenly into $\begin{array}{r}x\end{array}$ , then $\begin{array}{r}x\end{array}$ is an even number.
    ::报表3:如果2平均分为x,则x为偶数。
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  • Statement 4: I’ll be a millionaire when I win the lottery.
    ::报表4:我中彩票时将成为百万富翁。
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  • Statement 5: All equiangular triangles are equilateral.
    ::报表5:所有等角三角均为等边形。

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  Statements 1 and 3 are written in the “if-then” form. The hypothesis of Statement 1 is “you work overtime.” The conclusion is “you’ll be paid time-and-a-half.” Statement 2 has the hypothesis after the conclusion. If the word “if” is in the middle of the statement, then the hypothesis is after it. The statement can be rewritten: If the weather is nice, then I will wash the car. Statement 4 uses the word “when” instead of “if” and is like Statement 2. It can be written: If I win the lottery, then I will be a millionaire. Statement 5 “if” and “then” are not there. It can be rewritten: If a triangle is equiangular, then it is equilateral.
  ::报表1和报表3以“如果当时”的形式写成。报表1的假设是“你加班工作 ” 。结论是“你会得到报酬。 ” 。 报表2在结论之后有假设。如果“如果”一词在声明中间,则假设在声明之后。声明可以改写:如果天气良好,那么我会洗车。声明4使用“当”一词,而不是“如果”一词,就像报表2。可以写:如果我赢了彩票,那么我就是一个百万富翁。声明5“如果”和“当时”没有存在。可以改写:如果三角形是等角,那么它就是等角。

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  What if you were given a statement like "All squares are rectangles"? How could you determine the hypothesis and conclusion of this statement?
  ::万一你得到一个像"所有方形都是矩形"这样的声明呢?

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  Examples
  ::实例

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  Example 1
  ::例1

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  Determine the hypothesis and conclusion: I'll bring an umbrella if it rains.
  ::确定假设和结论:如果下雨,我会带伞。

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  Hypothesis: "It rains." Conclusion: "I'll bring an umbrella."
  ::假设:"下雨了。"结论:"我会带伞。"

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  Example 2
  ::例2

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  Determine the hypothesis and conclusion: All right angles are $\begin{array}{r}{90}^{\circ }\end{array}$ .
  ::确定假设和结论:所有右角度为 90。

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  Hypothesis: "An angle is right." Conclusion: "It is $\begin{array}{r}{90}^{\circ }\end{array}$ ."
  ::假设:"一个角度是对的。"结论:"这是90"。

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  Example 3
  ::例3

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  Use the statement: I will graduate when I pass Calculus.
  ::使用声明:我通过微积分后将毕业。

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  Rewrite in if-then form and determine the hypothesis and conclusion.
  ::以当时的形式重写,并确定假设和结论。

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  This statement can be rewritten as If I pass Calculus, then I will graduate. The hypothesis is “I pass Calculus,” and the conclusion is “I will graduate.”
  ::这句话可以被改写为如果我通过了微积分,然后我将毕业。 假设是“我通过了微积分 ” , 结论是“我将毕业 ” 。

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  Example 4
  ::例4

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  Use the statement: All prime numbers are odd.
  ::使用语句:所有质数都是奇数。

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  Rewrite in if-then form, determine the hypothesis and conclusion, and determine whether this is a true statement.
  ::以当时的形式重写,确定假设和结论,并确定这是否真实。

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  This statement can be rewritten as If a number is prime, then it is odd. The hypothesis is "a number is prime" and the conclusion is "it is odd". This is not a true statement (remember that not all conditional statements will be true!) since 2 is a prime number but it is not odd.
  ::此语句可以重写为如果一个数字是正数, 那么是奇数 。 假设是“ 一个数字是正数 ” , 结论是“ 奇数 ” 。 这不是一个真实的语句( 记住并非所有有条件的语句都是真实的! ) , 因为 2 是正数, 但并不奇怪 。

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  Example 5
  ::例5

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  Determine the hypothesis and conclusion: Sarah will go to the store if Riley does the laundry.
  ::确定假设和结论:莎拉会去商店 如果莱利洗衣服。

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  The statement can be rewritten as "If Riley does the laundry then Sarah will go to the store." The hypothesis is "Riley does the laundry" and the conclusion is "Sarah will go to the store."
  ::声明可以改写为“如果Riley洗衣服,Sarah会去商店。” 假设是“Riley洗衣服”,结论是“Sarah会去商店。”

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  Review
  ::回顾

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  Determine the hypothesis and the conclusion for each statement.
  ::确定每一声明的假设和结论。

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  1. If 5 divides evenly into $\begin{array}{r}x\end{array}$ , then $\begin{array}{r}x\end{array}$ ends in 0 or 5.
     ::如果 5 平分为 x, 则 x 以 0 或 5 结尾 。
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  2. If a triangle has three congruent sides, it is an equilateral triangle.
     ::如果三角形有三个相容面,则是一个等边三角形。
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  3. Three points are coplanar if they all lie in the same plane.
     ::如果它们都在同一架飞机上,三点是共平面的。
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  4. If $\begin{array}{r}x=3\end{array}$ , then $\begin{array}{r}{x}^2=9\end{array}$ .
     ::如果 x=3, 那么 x2=9 , 那么 x2=9 。
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  5. If you take yoga, then you are relaxed.
     ::如果你采取瑜伽, 那么你放松。
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  6. All baseball players wear hats.
     ::所有棒球运动员都戴帽子
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  7. I'll learn how to drive when I am 16 years old.
     ::我16岁时会学会开车
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  8. If you do your homework, then you can watch TV.
     ::如果你做功课,你就可以看电视了。
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  9. Alternate interior angles are congruent if lines are parallel.
     ::如果线条平行, 替代的内部角度是相似的 。
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  10. All kids like ice cream.
      ::所有的孩子都喜欢冰淇淋

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源