[Solved]: Predicate Logic Notation: What does a "dot" mean?

Problem Detail: 

What does a dot (.) mean in predicates?

$\forall a \in A. \exists d \in D. H(a,d)$

Especially, how is the above different to

$ \exists d \in D. \forall a \in A. H(a,d)$

I've never seen this used in German lecture scripts.

Asked By : nxrd

Answered By : David Richerby

The dot just means "such that"; it's often omitted.

The difference between the two formulas is the difference between "everybody has a mother" and "there is somebody who is everybody's mother."

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Question Source : http://cs.stackexchange.com/questions/60072