MAT2612 ASSIGNMENT 2 SOLUTIONS 2026

MAT2612 Assignment 2 solutions 2026
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Question 1

Given:

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


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

A relation is a function if every element of the domain is paired with exactly one element
in the codomain.

Checking the first coordinates:

𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓


Each element appears exactly once.

Therefore, R is a function from A to A.

Answer: Yes, because every element of A has exactly one image.



1.2 Is R an everywhere defined function?

An everywhere defined function means every element of A has an image.

The domain elements are:

𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓


All elements appear as first coordinates.

Therefore, R is everywhere defined.

Answer: Yes, because every element of A is mapped to an element of A.