Which term best describes the statement given below? If x = y and y = z, then x = z. A. Contrapositive statement B. Converse statement O C. Inverse statement D. A syllogism
The Correct Answer and Explanation is :
The correct answer is D. A syllogism.
Explanation:
A syllogism is a type of logical reasoning where a conclusion is drawn from two given or assumed propositions (premises). These premises must follow a logical structure to reach a conclusion. The example in your question follows this exact reasoning pattern:
- Premise 1: If ( x = y )
- Premise 2: If ( y = z )
- Conclusion: Therefore, ( x = z )
This structure is a syllogism because it involves two premises and a conclusion that logically follows from them. Specifically, the form of the syllogism is based on the transitive property in mathematics, which states that if ( a = b ) and ( b = c ), then ( a = c ).
In your case:
- ( x = y ) (First premise)
- ( y = z ) (Second premise)
- Thus, ( x = z ) (Conclusion)
This reasoning process is a classic example of syllogistic reasoning, where the relationship between ( x ), ( y ), and ( z ) is deduced logically.
Explanation of Other Options:
- A. Contrapositive statement: This refers to the logical negation of a statement and its converse. For example, the contrapositive of “If ( p ), then ( q )” is “If not ( q ), then not ( p ).”
- B. Converse statement: This involves reversing the order of the terms in a conditional statement. The converse of “If ( p ), then ( q )” is “If ( q ), then ( p ).”
- C. Inverse statement: This involves negating both the hypothesis and conclusion of a conditional statement. The inverse of “If ( p ), then ( q )” is “If not ( p ), then not ( q ).”
In contrast to these options, a syllogism clearly fits the reasoning pattern used in the question.