# Is it a standard to say that $a \oplus a_{\small 1}=0$ or $a \veebar a_{\small 1}=0$?

I am trying to express the following:

$a$ or $a_{\small 1}=0$ but only one of them equals zero.

so if $a=0$ then $a_{\small 1}\neq 0$ and if $a\neq 0$ then $a_{\small 1}=0$.

And I'm looking for a standard way to say that, from my little background in logic, I remember the logical operator xor which truth table fit my purposes. So is it ok to use any of the following notations?

$$a \oplus a_{\small 1}=0$$

$$a \veebar a_{\small 1}=0$$

• I would use the notation $$(a = 0) \oplus (a_1 =0).$$ You could always define your own notation. For example, let $Z(a,b,c):= (a=c) \oplus (b = c)$. – Kris Williams May 14 '13 at 2:45

Both symbols are variously used to denote XOR

But it would need to be expressed thusly:

$$(a = 0) \oplus (a_1 = 0)$$

or

$$(a = 0) \veebar (a_1 = 0)$$

And NOT, e.g., $$a \oplus a_1 = 0$$

• I know. I just shown both symbols because perhaps there's a defined standard with one of them and the other isn't used because it's already used in another math field. – Billy Rubina May 14 '13 at 2:46
• I think in either case, it would be good to reference either of the symbols you choose as representing "exclusive or": $\veebar$ may be more easily understood, given its similarity to $\lor$. But both are known, just not used terribly often in math. Sometimes you just see it "spelled out" as $\;p \lor q \land \lnot (p \land q)$ – Namaste May 14 '13 at 2:59
• Always nice and clear writeups! +1 – Amzoti May 14 '13 at 4:39