The type of proof you are referring to is known as "modus ponens." Modus ponens is a form of argument where if we have a conditional statement $ p \rightarrow q $ (if $ p $ then $ q $) and we know that $ q $ is true, we can conclude that $ p $ must also be true. This logical reasoning is fundamental in various fields, including mathematics and philosophy, and illustrates the process of deriving a conclusion based on premises.

In more formal terms, a proof using modus ponens involves the structure:

1. Premise 1: $ p \rightarrow q $ (if $ p $, then $ q $)
2. Premise 2: $ q $ is true
3. Conclusion: Therefore, $ p $ is true.

This structure helps establish the validity of arguments and is a critical component in logical reasoning and deductive proofs.

Question

The type of proof you are referring to is known as "modus ponens." Modus ponens is a form of argument where if we have a conditional statement $ p \rightarrow q $ (if $ p $ then $ q $) and we know that $ q $ is true, we can conclude that $ p $ must also be true. This logical reasoning is fundamental in various fields, including mathematics and philosophy, and illustrates the process of deriving a conclusion based on premises.

In more formal terms, a proof using modus ponens involves the structure:

1. Premise 1: $ p \rightarrow q $ (if $ p $, then $ q $)
2. Premise 2: $ q $ is true
3. Conclusion: Therefore, $ p $ is true.

This structure helps establish the validity of arguments and is a critical component in logical reasoning and deductive proofs.

Knowee AI · Accepted Answer

The type of proof you are referring to is known as "modus ponens." Modus ponens is a form of argument where if we have a conditional statement $ p \rightarrow q $ (if $ p $ then $ q $) and we know that $ q $ is true, we can conclude that $ p $ must also be true. This logical reasoning is fundamental in various fields, including mathematics and philosophy, and illustrates the process of deriving a conclusion based on premises.

In more formal terms, a proof using modus ponens involves the structure:

1. Premise 1: $ p \rightarrow q $ (if $ p $, then $ q $)
2. Premise 2: $ q $ is true
3. Conclusion: Therefore, $ p $ is true.

This structure helps establish the validity of arguments and is a critical component in logical reasoning and deductive proofs.

A proof that p → q is true based on the fact that q is true, such proofs are known as ___________

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A proof that p → q is true based on the fact that q is true, such proofs are known as ___________

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