Logical updates…

Good to know, for HTML, at least: 

∃ is {& exist;}
∀ is {& forall;}
↔ is {& harr;}
≡ is {& equiv;}
∴ is {& there4;}
□ is {& #9633;}
◊ is shift+alt/option v (auf 'ner deutschen Tastatur) or ◊ {& loz;}
∩ {& #x2229;} (Where members of set X are members of A both and B.)
U is… U (Where members of set X are members of either A or B.)

[Remove space between & and the sequalia.]

Here are my poor man's HTML-free stabs at it…

$x : there is an x
A*x : for all x
<--> : iff
=* : means, is semantically entailed by
‹› : it is contingent that
[] : it is necessary that
Ω* : intersection of
∆· : therefore

All of these only work (or work best) on a German keyboard (as I have set on my Mac).

So, let's try this again…

For : "Every dog (Dx) is loved by (Lyx) at least one man (My). herefore, at least one man loves every dog (~∀y∃x(~∃x~Lyx)) loves every dog (Dx)." 

Valid or invalid? Show your work!

~(Dx --> ($y(My ^ Lyx)) ^ --> (A*x$x(Dx ^ My ^ Lyx)))