QQuestionMathematics
QuestionMathematics
Which term best describes the statement given below?
If a≤b and b≤c, then a≤c.
A. Contrapositive statement
B. A syllogism
C. Inverse statement
D. Converse statement
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Answer
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Step 1:I'll solve this step by step, focusing on the logical reasoning:
Step 2:: Understand the given statement
The statement $$a \leq b$$ and $$b \leq c$$ implies $$a \leq c$$ is a fundamental property of inequality.
Step 3:: Analyze the logical structure
This statement demonstrates the transitive property of inequality, which is a key principle in mathematical reasoning.
Step 4:: Examine the given options
A. Contrapositive statement B. A syllogism C. Inverse statement D. Converse statement
Step 5:: Define each term
- Syllogism: A form of logical reasoning with two premises and a conclusion - Contrapositive: Negating both parts of an implication and reversing their order - Inverse: Negating both parts of an original statement - Converse: Swapping the if and then parts of a conditional statement
Step 6:: Identify the correct classification
This statement represents a syllogism, which is a logical argument that uses deductive reasoning to reach a conclusion based on two premises.
Final Answer
A syllogism Explanation: The statement follows the classic syllogistic form: - Premise 1: a \leq b - Premise 2: b \leq c This is a perfect example of a syllogism in mathematical logic.
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