Quantifiers for multiple variables?

Question

I know about the universal quantifier(translated to "for all") $\forall$ and the existential quantifier(there exists) $\exists$. But I am not sure what the correct way is to use them for multiple multiple variables.

For example:

1. How would you use the quantifiers to express "for all x, y, c..."?

2. How would you use the quantifiers to express "for all x, y, c in $\mathbb{R}$..."?

3. How would you use the quantifiers to express "for all x, y, c in $\mathbb{R}$, there exists a, b such that..."?

Answer 1

Both

1. $\forall x,y,c \dots$
2. $\forall x,y,c \in \mathbb R \dots$
3. $\forall x,y,c \in \mathbb R: \exists a, b: \dots$

and

1. $\forall x, \forall y, \forall c \dots$
2. $\forall x \in \mathbb R, \forall y \in \mathbb R, \forall c \in \mathbb R \dots$
3. $\forall x \in \mathbb R, \forall y \in \mathbb R, \forall c \in \mathbb R: \exists a, \exists b: \dots$

are acceptable.