First-Order Predicate Logic on example

Question

I have a question if First Order Predicate Logic always has to include quantifiers? E.g. in the sentence, A black dog bit a small child, would it be:

Bit(dog, child)

or

∀: Bit (dog, child) ?

Therefore, in the sentence All the children who live in Otley know each other, would it be:

∃: Know(x, y)

or

∃: Know (x, child) ?

Answer 1

Fill in the blanks with suitable predicates.

Example 1

There exists x and y such that BlackDog(x) and ___________________ and ________________.

Example 2

For all x and y, if OtleyChild(x) and _________________ then ___________________ and ______________________.