Which of the following types of statements can explain the steps of a proof? Check all that apply.
A. Corollaries
B. Conjectures
C. Definitions
D. Postulates
A C & D
E. Dad jokes
Just kidding! The correct answers are A. Corollaries, C. Definitions, and D. Postulates. These types of statements are used to explain the steps of a proof and provide the necessary information and assumptions to carry out the proof successfully. So, you can rule out B. Conjectures because those are more like educated guesses or ideas that need to be proven, not steps in a proof.
The types of statements that can explain the steps of a proof are:
A. Corollaries - Corollaries are derived from theorems and provide further consequences or implications of the main theorem. They can often be used to explain the logical steps in a proof.
C. Definitions - Definitions establish the meaning of terms and provide the basis for understanding concepts used in the proof. They can help explain the steps by clarifying the relevant variables or entities involved.
D. Postulates - Postulates, also known as axioms, are fundamental assumptions or principles that are accepted without proof. They can be used to explain the foundational steps in a proof.
Conjectures, on the other hand, are statements that have not yet been proven and are more speculative in nature. They are not suitable for explaining the steps of a proof. Therefore, option B would not be applicable to this question.
B and C
Answer
Conjectures
Postulates