Can we say that an element is not a subset of a set? I am creating a multiple choices question for students that should be as follows:

Which of the following is true?

1) $8\in \mathbb{Z^{+}}$

2) $8\notin \mathbb{Z^{+}}$

3) $8\subset \mathbb{Z^{+}}$

4) $8 \not\subset \mathbb{Z^{+}}$

Should choices Number (1) and (4) be considered as valid answers?
My understanding is that we can't deal with an element with either $\subset$ or $\not\subset$.

Please give me references supporting your answer if there.
Yes, an element of a set can be a subset of that set. 

Think of $\varnothing\in\{\varnothing\}$ and $\varnothing\subset\{\varnothing\}$, where $\varnothing$ denotes the empty set.

The answer to your multiple choice question depends on how $\mathbb Z_+$ and $8$ are defined.

A possible construction exists with $\mathbb Z_+=\{1,2,3,\dots,8,\dots\}$ and $8=\{1,2,3,4,5,6,7\}$.

In that case $8\in\mathbb Z_+$ and $8\subset\mathbb Z_+$.
For me the option 1 is valid, for options 3 and 4 proper notation of set isn't used. If we require to represent a set with elements then the elements should be surrounded by curly braces . Hence 8 doesn't represents a set therefore 3 and 4 options are invalid.

This wikipedia post suggests the notation used for set elements