How to describe the given relation on A using set builder notation?

Question

A = {0, 1, 2, 3, 4}

S = { (0, 4), (1, 3), (2, 2), (3, 1), (4, 0) }

S is a relation on set A. How do we describe this relation?

Is the following description correct?

S = {(x,y): x ∈ A, y ∈ A, x + y is even}

And can we write x,y ∈ A at once or we have to write x ∈ A, y ∈ A ?

Does the relation have to contain all the even sums to be described in above way ?

To address your third question, you can write $(x,y)\in A^2$. — orion2112, Apr 04 '18 at 06:34

score 1 · Answer 1 · answered Apr 04 '18 at 06:34

1

No, it is not correct, otherwise $(2,4) \in S$.

Guide:

Notice that $0+4=1+3 = \ldots = 4+0$.

answered Apr 04 '18 at 06:34

Siong Thye Goh

I can only observe a pattern that x is increasing from 0 to 4 and y decreasing from 4 to 0. But not able to describe it. – Brainy Prb Apr 04 '18 at 07:07
they always sum to a number, $0+4=4$, $1+3=4$, $\ldots$. – Siong Thye Goh Apr 04 '18 at 07:11
oops, thank you – Brainy Prb Apr 04 '18 at 07:27

1 Answers1