status: DONE
created: 2023-12-23T02:12
updated: 2024-06-11T01:14
publish: True

Discrete Mathematics Tutorial

Question 1

Assume is an integer. Prove that if is odd, then n is odd.

NO.	Steps	Reasons
1.	n is odd	Assumption
2.	n is even	Definition of even
3.	Let n = 2k for an integer k.	Assumption
4.	3n^2+2=16k^2+2 =2(6k+1)	Substitution and calculation
5.	is even	Definition of even
6.	If n is not odd, then is even	Deduction
7.	If is odd, then n is odd.	Contraposition

Prove that is a tautology.