Questions: Which of the following require proof in a logical system? Check all that apply. A. Corollaries B. Postulates C. Theorems D. Axioms

Transcript text: Which of the following require proof in a logical system? Check all that apply. A. Corollaries B. Postulates C. Theorems D. Axioms

Solution

Solution Steps

Step 1: Identify the Component

The component in question is ^A^, which is classified as a ^Corollaries^.

Step 2: Determine the Category

Since ^A^ is a ^Corollaries^, it must be ^proved^ within the logical system. It is a derived statement that follows from previously established axioms, postulates, or other theorems.

Final Answer:

^A^ is categorized as ^Require proof^ within the logical system.

Step 1: Identify the Component

The component in question is ^B^, which is classified as a ^Postulates^.

Step 2: Determine the Category

Since ^B^ is a ^Postulates^, it falls under the category of components that are ^accepted without proof^. These are foundational elements that provide a basis for further reasoning and deduction within the logical system.

Final Answer:

^B^ is categorized as ^Accepted without proof^ within the logical system.

Step 1: Identify the Component

The component in question is ^C^, which is classified as a ^Theorems^.

Step 2: Determine the Category

Since ^C^ is a ^Theorems^, it must be ^proved^ within the logical system. It is a derived statement that follows from previously established axioms, postulates, or other theorems.

Final Answer:

^C^ is categorized as ^Require proof^ within the logical system.

Step 1: Identify the Component

The component in question is ^D^, which is classified as a ^Axioms^.

Step 2: Determine the Category

Since ^D^ is a ^Axioms^, it falls under the category of components that are ^accepted without proof^. These are foundational elements that provide a basis for further reasoning and deduction within the logical system.

Final Answer:

^D^ is categorized as ^Accepted without proof^ within the logical system.

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