MAT2613 Assignment 1 solutions 2026

MAT2613 Assignment 1 solutions 2026
ASSIGNMENT 01
Closing Date: 30 April 2026
Total Marks: 100
UNIQUE ASSIGNMENT NUMBER: 197154
All questions solved with full working. If need assignment or exam help any module
reach me 0793226427




AT2613 Assignment 01 Complete Solutions

, Question 1

Given statement:

𝐴:If 𝑛2 is odd, then 𝑛 is odd.


(1.1) Contrapositive

The contrapositive of 𝑃 ⇒ 𝑄is ¬𝑄 ⇒ ¬𝑃.

• 𝑃: 𝑛2 is odd

• 𝑄: 𝑛is odd

Thus:

¬𝑄: 𝑛 is even, ¬𝑃: 𝑛2 is even


Contrapositive:

If 𝑛 is even, then 𝑛2 is even.


Proof:

Let 𝑛 = 2𝑘, where 𝑘 ∈ ℤ.

𝑛2 = (2𝑘)2 = 4𝑘 2 = 2(2𝑘 2 )


Thus, 𝑛2 is even.

Conclusion:

The contrapositive is true, hence the original statement is true.



(1.2) Converse

The converse is:

If 𝑛 is odd, then 𝑛2 is odd.


Proof:

Let 𝑛 = 2𝑘 + 1, 𝑘 ∈ ℤ.

𝑛2 = (2𝑘 + 1)2 = 4𝑘 2 + 4𝑘 + 1 = 2(2𝑘 2 + 2𝑘) + 1