Deciding if a statement is true or false for given sets Given the sets: 

$A = \{a,b,c\},\enspace B = \{a,b,A,C\},\enspace C = \{a,c\},\enspace D = \{A,B,C\},\enspace and\enspace G = \{A,B,C,D\}$

How can I determine if the following statement is true or false:

$∃x ∈ D : ∃y ∈ x : y ∉ B ∪ x$    

First of all, please correct me if I'm wrong, but it seems to me that the symbols used in the statements are inconsistent. Say, if some element $y$ belongs to $x$, I assume that $x$ should be a set itself. After taking a quick look at the problem, one can conclude that sets are denoted by capital letters. So I expect $x$ to be $X$ instead.
Apart from this nuisance, I wonder if my translation into English is correct. I'm reading the statement as

For some element $x$ (which is actually set $X$) from set $D$, there is some element $y$ from $x$ such that $y$ does not belong to the union of set $B$ with $x$.

So if my interpretation of the mathematical notation is correct, I go on to assume that

$y ∉ B ∪ x\quad ≡\quad y ∉ \{x,a,b,A,C\}$ (all distinct elements combined)  

Then I'm really confused. How can $∃y ∈ x$ and at the same time $y ∉ \{x,a,b,A,C\}$? Does it mean that the statement is false?

The notation is correct. maybe that the use of a capital $X$ for the sets can be better, but it's not necessary.
The statement is false: $y \in x \Rightarrow y \in B\cup x$
