Notation for appending the same element to each set of a set of sets

Question

If I had a set $A = \{\{1, 2\}, \{2, 3\}, \{1, 3\}\}$, how would I go about notating the set $B = \{\{1, 2, 4\}, \{2, 3, 4\}, \{1, 3, 4\}\}$ without explicitly writing out $B$?

More generally, if I had a set of sets $A$, how would I denote the set $B$, the set obtained by appending/adding the same element (not in any of the current sets in $A$, of course), to each element of $A$?

Answer 1

$B = \{a \cup \{4\} \mid a \in A\}$.