
Correct syntax
Hello
Could you tell me which one is correct? If none of them are, could you write the correct format?
$\displaystyle \exists$j j $\displaystyle \in$ myset
$\displaystyle \exists$j, j $\displaystyle \in$ myset
$\displaystyle \exists$ j $\displaystyle \wedge$ j $\displaystyle \in$ myset
which I could not get to display properly, but it is
$\displaystyle \exists$ j logical and j $\displaystyle \in$ myset
Thank you all!

Re: Correct syntax
∃j ∧ j ∈ myset is wrong because ∧ has to join two wellformed formulas, and ∃j is not a complete formula. Whether to put a comma after ∃j is purely a question of definitions and conventions.
In the most unfolded form, the statement "there exists a j in myset such that P(j)" can be written as ∃j (j ∈ myset ∧ P(j)). Often it is abbreviated to ∃j ∈ myset, P(j). However, this refers to unsorted logic, where variables don't have an intrinsic range, or sort, and j ∈ myset is a proposition. There are other logic languages where one must specify a variable's sort when the variable is introduced. Then ∃j ∈ myset or ∃j : myset is an indivisible expression that does not stand for ∃j (j ∈ myset ∧ ...).