Contrapositives are confusing

  • Context: High School 
  • Thread starter Thread starter PsychonautQQ
  • Start date Start date
  • Tags Tags
    Confusing
Click For Summary
SUMMARY

The discussion centers on the application of contrapositives in mathematical logic, specifically regarding the statement "if n^2 + 2 is prime, then 3|n." The contrapositive presented is "if 3 does not divide n, then n^2 + 2 is not prime." Participants confirm that demonstrating the truth of the contrapositive effectively validates the original statement. The consensus is that the approach taken is correct and appropriate for proving the original assertion.

PREREQUISITES
  • Understanding of mathematical logic and implications
  • Familiarity with prime numbers and divisibility
  • Knowledge of contrapositives in logical statements
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of prime numbers and their implications in number theory
  • Learn about logical equivalences and their applications in proofs
  • Explore examples of contrapositives in mathematical proofs
  • Practice proving statements using contrapositives in various mathematical contexts
USEFUL FOR

Students of mathematics, educators teaching logic and proofs, and anyone interested in enhancing their understanding of logical implications and contrapositives.

PsychonautQQ
Messages
781
Reaction score
10
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?
 
Physics news on Phys.org
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.
 
  • Like
Likes   Reactions: PsychonautQQ

Similar threads

Undergrad Contrapositive of theorem and issue with proof
  • · Replies 5 ·
Replies
5
Views
2K
MHB Proof by induction - Really confused
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad On the meaning of logical implication within specific context/models
  • · Replies 22 ·
Replies
22
Views
4K
High School Baccarat math and beating the edge
  • · Replies 3 ·
Replies
3
Views
4K
MAT385-Proof by contraposition
  • · Replies 8 ·
Replies
8
Views
3K
Prove True/False that n^3-n is Always Divisible By 6
  • · Replies 4 ·
Replies
4
Views
3K
MHB Can L-Shaped Tiles Fit Perfectly on a 2xn Board If n Is Not Divisible by 3?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Is the Intersection of Intervals Empty?
  • · Replies 8 ·
Replies
8
Views
2K
Proofs involving negations and conditionals
  • · Replies 2 ·
Replies
2
Views
3K
Graduate The Current State of Mathematical Rigour
  • · Replies 6 ·
Replies
6
Views
2K