Contrapositives are confusing

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In summary, the conversation revolves around understanding and applying contrapositives in order to show that if n^2+2 is prime, then 3|n. The speaker is unsure if they are correctly demonstrating the contrapositive and seeking confirmation.
  • #1
PsychonautQQ
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I'm a bit confused on how to apply contrapositives... This isn't for homework but I'm attempting to show that if n^2 + 2 is prime that 3|n.

I'm wondering if this is an appropriate time for me to show the contrapositive of the statement to be true, therefore the original statement to be true.

Contrapostive: if 3 does not divide n, then n^2+2 is not prime.

I know how to show this contrapositive to be true...

Am I doing this right?
 
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  • #2
PsychonautQQ said:
I'm a bit confused on how to apply contrapositives... This isn't for homework but I'm attempting to show that if n^2 + 2 is prime that 3|n.

I'm wondering if this is an appropriate time for me to show the contrapositive of the statement to be true, therefore the original statement to be true.

Contrapostive: if 3 does not divide n, then n^2+2 is not prime.

I know how to show this contrapositive to be true...

Am I doing this right?
Yes.
 
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Related to Contrapositives are confusing

What is a contrapositive?

A contrapositive is a statement that is formed by negating both the hypothesis and conclusion of a conditional statement and reversing their order. It is logically equivalent to the original statement.

Why are contrapositives confusing?

Contrapositives can be confusing because they involve a negation and a reversal of the original statement, making it difficult for some people to understand the logical relationship between the two statements.

How do I identify a contrapositive?

To identify a contrapositive, look for a statement that is formed by negating and reversing the hypothesis and conclusion of a conditional statement. It will have the same truth value as the original statement.

What is the purpose of using contrapositives?

The purpose of using contrapositives is to prove or disprove a statement by showing that its contrapositive is true or false. It can also help to clarify the logical relationship between two statements.

Can you give an example of a contrapositive?

Yes, an example of a contrapositive is: "If it is raining, then the ground is wet." The contrapositive of this statement is: "If the ground is not wet, then it is not raining."

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