A relation (T(x, y)) becomes a proposition when its variables are bound to objects (T(Dan, M1)). After the variables are bound to objects it can be determined to be either true or false.

University of Michigan - Ann Arbor

Explicitly defines objects and relations among those objects. For example take the following sentence:
- "Dan is taller than both his mothers, but they’re the same height.”

The objects: 
- Dan
- M1 = Mother 1
- M2 = Mother 2

The relations:
- T(x, y) = "x is taller than y"

The predicate:
- T(Dan, M1) $$\land$$ T(Dan, M2) $$\land$$ $$\lnot$$ T(M1, M2) $$\land$$ $$\lnot$$ T(M2, M1)

Predicate logic

University of Michigan EECS 203 Lecture Notes

When does a relation become a proposition?

Relations can have a single argument.

"If you are happy, I am happy"

Relation:
H(x) = "x is happy"

objects:
- y = you
- I = I

Predicate:
- H(y) $$\rightarrow$$ H(I)

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