To determine if the argument is valid, let's break it down using the information provided.
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Given Statement: "If a geometric figure starts at a point and extends forever in one direction, then it is a ray."
- This is a conditional (if-then) statement.
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Stated Fact: "is a ray."
- This appears to be incomplete but implies that we are identifying some geometric figure as a ray.
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Conclusion: "starts at one point and extends forever in one direction."
- This is the conclusion drawn based on the previous statements.
The given statement can be denoted as:
- If \( P \) (a geometric figure starts at a point and extends forever in one direction), then \( Q \) (it is a ray).
The fact that "is a ray" can be interpreted as asserting \( Q \).
Now, to apply the Law of Detachment: If \( P \) implies \( Q \) (which it does), and we know \( Q \) is true (the figure is a ray), we can conclude that \( P \) (it starts at one point and extends forever in one direction) must also be true.
Thus:
- Since we know a geometric figure is a ray (true), we can conclude that it starts at one point and extends forever in one direction (also true) based on our original statement.
Thus, the correct answer would be: Yes. This argument uses the Law of Detachment.