Is there a mathematical symbol for "and"?

Question

I have a statement as such:

$\mathbb{Z_+} \triangle E = \{ x \in \mathbb{Z_+} : x \space \% \space 2 \neq 0 \space and \space x \in \mathbb{Z} : x < 0 \space and \space x \space \% \space 2 = 0 \}$

($E$ represents all even numbers, positive and negative. Not important to the actual question, but it is important to the statement above.)

My question is: is there any way I can get those "and"s out of my statement? They seem so out of place. Is there any notation for "and"?

Bonus: Is my statement correct?

Answer 1

There's the usual &. And there's: $\land$, but this is only used in propositional logic; so to use that you should make your statement too formal in shape in order for it not to look weird. It might confuse some as well because it may mean different things in different situations.

Also, if you have been doing advanced math for too long, "," might magically become a symbol for "and", though the same symbol is sometimes used as "or" and "such that" as well; it depends on the context (and can be understood what to mean from there).

"Is my statement true?" Yes.

Answer 2

Assuming that $\mathbb{Z}_{+}$ has the standard meaning of $$\mathbb{Z}_{+}=\{\text{positive integers}\}=\{x\in\mathbb{Z}:x>0\}$$ then your answer is not quite right, since $$\begin{align*} \mathbb{Z}_{+}\mathrel{\triangle}E&=\{x\in\mathbb{Z}_{+}:x\notin E\}\cup\{x\in E:x\notin\mathbb{Z}_{+}\}\\\\ &=\{x\in\mathbb{Z}_{+}:x\not\equiv0\bmod 2\}\cup\{x\in\mathbb{Z}:x\in E\wedge x\notin\mathbb{Z}_{+}\}\\\\ &=\{x\in\mathbb{Z}_{+}:x\not\equiv0\bmod 2\}\cup\{x\in\mathbb{Z}:x\equiv 0\bmod 2\wedge x\not>0\}\\\\ &=\{x\in\mathbb{Z}_{+}:x\not\equiv0\bmod 2\}\cup\{x\in\mathbb{Z}:x\equiv 0\bmod 2\wedge x\leq 0\} \end{align*}$$ The error is that "not positive" doesn't mean "negative". Your set misses the element $0$.