Which Term Best Describes the Statement Given Below?
In logic, there are four terms that can be used to describe a statement:
- Original statement: The original statement is the statement that is given. In this case, the original statement is "If x = y and y = z, then x = z."
- Converse statement: The converse statement is the statement that reverses the order of the original statement’s two propositions. In this case, the converse statement is "If x = z, then y = z."
- Inverse statement: The inverse statement negates both propositions of the original statement. In this case, the inverse statement is "If x ≠ z, then y ≠ z."
- Contrapositive statement: The contrapositive statement negates both propositions of the original statement and reverses their order. In this case, the contrapositive statement is "If y ≠ z, then x ≠ z."
To determine which term best describes the statement given below, we can use the following steps:
- Identify the original statement.
- Reverse the order of the original statement’s two propositions.
- Negate both propositions of the original statement.
- Reverse the order of the negated propositions.
If the resulting statement is equivalent to the original statement, then the term converse statement is the correct answer. If the resulting statement is equivalent to the contrapositive statement, then the term contrapositive statement is the correct answer. If the resulting statement is equivalent to the inverse statement, then the term inverse statement is the correct answer.
In the case of the statement "If x = y and y = z, then x = z," the converse statement is "If x = z, then y = z." This statement is not equivalent to the original statement, so the term converse statement is not the correct answer.
The inverse statement is "If x ≠ z, then y ≠ z." This statement is also not equivalent to the original statement, so the term inverse statement is not the correct answer.
The contrapositive statement is "If y ≠ z, then x ≠ z." This statement is equivalent to the original statement, so the term contrapositive statement is the correct answer.
Therefore, the answer to the question "Which term best describes the statement given below?" is contrapositive statement.
Additional Questions
Here are some additional questions that can be used to test understanding of the four terms:
- What is the difference between a converse statement and a contrapositive statement?
- How can you determine which term best describes a statement?
- What are the implications of using the contrapositive statement?
Answers
- The difference between a converse statement and a contrapositive statement is that the converse statement reverses the order of the propositions in the original statement, while the contrapositive statement negates both propositions and reverses their order.
- **To determine which term best describes a statement, you can use the following steps:
- Identify the original statement.
- Reverse the order of the original statement’s two propositions.
- Negate both propositions of the original statement.
- Reverse the order of the negated propositions.
If the resulting statement is equivalent to the original statement, then the term converse statement is the correct answer. If the resulting statement is equivalent to the contrapositive statement, then the term contrapositive statement is the correct answer. If the resulting statement is equivalent to the inverse statement, then the term inverse statement is the correct answer.**
- The contrapositive statement is often used in logic because it is logically equivalent to the original statement. This means that if the contrapositive statement is true, then the original statement must also be true.
