Predicate logic, linear relation I've got a question about linear relations in predicate logic.
I've got the follow definition where R is a relation of x has a Relation to y.
$$\forall x \forall y(Rxy \vee x = y \vee Ryx)$$
How do I read this? Are there 3 formulas? Or just 2?
Also, what would be the correct answers to the question: Do the following sentences describe a linear relation?
(1) being an ancestor of . . . on the set of human beings,
(2) being a parent of . . . on the set of human beings,
(3) the ‘less than’ relation < on the natural numbers,
My answers would be False,False, False.

It's three.  Read it as: $\forall x\forall y \big((Rxy)\vee (x=y)\vee (Ryx)\big)$
This is true is at least one of those conditions is true for any pair of $(x,y)$.
It is false if there exists at least one pair $(x,y)$ such that none of those conditions are true.
The statement, "x is the ancestor of y, or x is y, or y is the ancestor of x", is false because x and y may be, for instance, siblings (or unrelated), in which case neither would be an ancestor of the other.
Contrast to $\forall x\in \mathbb{N},\forall y \in \mathbb{N}, (x<y)\vee(x=y)\vee(y<x)$.  Which is self evidently true since natural numbers are ordered.
