Question: In Exercises 21 624, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible. (See Example 5.)
21. If $x < -2$, then $|x| > 2$. If $x > 2$, then $|x| > 2$.
1. **State the problem:** We are given two conditional statements:
- If $x < -2$, then $|x| > 2$.
- If $x > 2$, then $|x| > 2$.
We need to use the Law of Syllogism to write a new conditional statement that follows from these.
2. **Recall the Law of Syllogism:**
The Law of Syllogism states that if "If $p$, then $q$" and "If $q$, then $r$" are true statements, then "If $p$, then $r$" is also true.
3. **Check if the Law of Syllogism applies:**
- First statement: If $x < -2$, then $|x| > 2$.
- Second statement: If $x > 2$, then $|x| > 2$.
The conclusion part ($q$) of the first statement is $|x| > 2$, but the hypothesis part ($p$) of the second statement is $x > 2$.
Since $q$ of the first statement ($|x| > 2$) is not the same as $p$ of the second statement ($x > 2$), the Law of Syllogism does not apply here.
4. **Conclusion:**
No new conditional statement can be formed using the Law of Syllogism from these two statements.
**Final answer:** No new conditional statement follows from the given pair using the Law of Syllogism.