Is this formula an atomic formula?

Question

For example, the formula $\forall x.\;P(x)\wedge∃y.\;Q(y,f(x))\vee∃z.\;R(z)$ contains the atoms

$$P(x),\;Q(y,f(x)),\;R(z) $$

I'm reading definition from wikipedia but I'm somehow confused if this whole statement is atomic formula

Answer 1

No. By definition, a formula is atomic if it is

• of the form $P(t_1, \ldots t_n)$, for an $n$-aray predicate $P$ and terms $t_1, \ldots t_n$, or
• of the form $t_1 = t_2$, for two terms $t_1, t_2$.

So an atomic formula is a simple predication or equality (assuming that your logic has the equality sign $=$).
Anything that has a connective or a quantifier in it is not an atomic formula.

Since $∀x. P (x) ∧ ∃y. Q (y, f (x)) ∨ ∃z. R (z)$ involves logical connectives ($\land, \lor$) as well as quantifiers ($\forall, \exists, \exists$), it is not atomic.

A formula that is not atomic is sometimes called complex.