Math

QuestionIdentify which items are accepted without proof in a logical system: A. Postulates, B. Definitions, C. Axioms, D. Theorems.

Studdy Solution

STEP 1

Assumptions1. We are working within a logical system. . We are considering the standard definitions of postulates, definitions, axioms, and theorems.

STEP 2

Consider the nature of each option.
A. Postulates These are statements that are assumed to be true without proof. They are the starting point for further reasoning and arguments.
B. Definitions These are not statements that can be true or false, but rather explanations of what a term means. They are accepted as they are.
C. Axioms These are statements that are accepted as true without proof, similar to postulates.
. Theorems These are statements that have been proven to be true based on axioms, postulates, and previously proven theorems.

STEP 3

Based on the nature of each option, we can conclude that postulates, definitions, and axioms are accepted without proof in a logical system, while theorems require proof.
So, the answer is A. Postulates, B. Definitions, and C. Axioms.

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