Which is the difference between the logical propositions $\exists a, b$ and $\exists a \exists b$?

Question

I was wondering if there is any difference between $\exists a,b$ and $\exists a \exists b$. I can't imagine there would be any but my homework uses them both.

Answer 1

The former abbreviates the latter, just as $$\exists x{\in}\mathbb R\;Px$$ abbreviates $$\exists x\,\big(x{\in}\mathbb R\land Px\big),$$ and $$\forall\;a,b$$ abbreviates $$∀a\,∀b.$$