MAT2612 Assignment 3 (872315)|EXPERT SOLUTIONS|2025

MAT2612
Assignment 3

Unique No: 872315
2025

, Based on Chapters 5 & 6 of prescribed textbook

ASSIGNMENT 03

Total Marks: 100

Unique no.:872315

Question 1 (8 marks)

R = {(a,e), (b,d), (c,c), (d,a), (e,b)} on A = {a,b,c,d,e,f}.

(1.1) Is R a function from A to A? (2 marks)

Answer: Yes, R is a function (a partial function).

Reason: A relation is a function if no element of the domain appears paired with two
different images. The first-coordinates in R are a,b,c,d,e each appears exactly once, so
no element maps to two different images. (The element f simply does not appear.)

(1.2) Is R an everywhere defined function? (2 marks)

Answer: No.

Reason: Everywhere defined (from A to A) requires every element of A to have an
image. Element f does not appear as a first coordinate, so R is not defined at f.

(1.3) Is R onto (surjective)? (2 marks)

Answer: No.

Reason: The set of images (second coordinates) is {e,d,c,a,b}. Element f of A is not an
image, so not every element of codomain A is hit.

(1.4) Is R one-to-one (injective)? (2 marks)

Answer: Yes.

Reason: All images {e,d,c,a,b} are distinct (no two different domain elements map to
the same codomain element). Thus R is injective (even though it is not everywhere
defined).