Discrete Relations: can't understand relation definition

[theRukus]

Homework Statement

Let Z be the set of all integers.

Then, S is a relation on the set Z x Z defined by:

for (a₁, a₂), (b₁, b₂) belong to Z x Z,

(a₁, a₂)S(b₁, b₂) <-> a₁b₂ = a₂b₁.

Homework Equations

The Attempt at a Solution

The actual problem is about symmetry, antisymmetry, transitivity, and reflexivity. I get all of those concepts. What I don't understand is,

What does (a₁, a₂)S(b₁, b₂) mean?


Thank you for any help.

 

[theRukus]

If anyone has anything close to an idea of what this could mean.. Please help. I just need a good guess so I can try the question, but I don't have a clue.

 

[Mark44]

S is the symbol for the relation. For example, (1, 2)S(2, 4) because 1*4 = 2*2. In this case the relation is that two ordered pairs are proportional. You could think of the ordered pairs as ratios: 1 is to 2 in the same ratio as 2 is to 4.