Final answer:
The correct match for the conditional statement and its counterparts is as follows: (1) Converse: If the intersection of two lines is a point, then they intersect. (2) Inverse: If two lines do not intersect, then their intersection is not one point. (3) Contrapositive: If the intersection of two lines is not one point, then the two lines do not intersect. The correct option is (D).
Step-by-step explanation:
In logic and mathematics, we often deal with conditional statements, which are typically written in the if-then form. Understanding the relations between such statements is crucial for various proofs and logical deductions. The question provided asks us to match each statement with the correct logical counterpart based on a given conditional statement.
The original conditional statement is: If two lines intersect, then their intersection is one point. From this original statement, we can derive three logical counterparts:
- Converse: If the intersection of two lines is a point, then they intersect.
- Inverse: If two lines do not intersect, then their intersection is not one point.
- Contrapositive: If the intersection of two lines is not one point, then the two lines do not intersect.
Now matching these to the options provided:
- Option (A): 1. converse, 2. contrapositive, 3. inverse
- Option (B): 1. inverse, 2. contrapositive, 3. converse
- Option (C): 1. contrapositive, 2. inverse, 3. converse
- Option (D): 1. converse, 2. inverse, 3. contrapositive
The correct answer is Option (D): The first statement is indeed the converse because it shows the condition and the result in reverse order. The second statement is the inverse because it negates both the hypothesis and the conclusion of the original conditional. Lastly, the third statement is the contrapositive since it negates and reverses the original conditional.