MAT2613
ASSIGNMENT 1
2025
, QUESTION 1
Solution:
1.1).
Contrapositive statement: If p is not even, then p2 is not divisible by 4
Suppose p is not even, which means p is odd, then
p = 2k + 1 for some integer k
Now
p2 = (2k + 1)2
= (2k + 1)(2k + 1)
= 4k 2 + 4k + 1
= 4(k 2 + k) + 1 (not divisible by 4)
Hence contrapositive statement is true
ASSIGNMENT 1
2025
, QUESTION 1
Solution:
1.1).
Contrapositive statement: If p is not even, then p2 is not divisible by 4
Suppose p is not even, which means p is odd, then
p = 2k + 1 for some integer k
Now
p2 = (2k + 1)2
= (2k + 1)(2k + 1)
= 4k 2 + 4k + 1
= 4(k 2 + k) + 1 (not divisible by 4)
Hence contrapositive statement is true
