OR vs XOR as fundamental logic gates Why are the standard logical connectives for languages AND and OR (and IMPLIES)? I would agree with the assertion that they are more natural in some way, easier to think about than connectives like NAND or XNOR. What I question is the choice of OR over XOR as a fundamental gate.
XOR behaves like addition of the integers mod 2, analogous to AND behaving as multiplication mod 2, which means that the pair behaves like the field of integers mod 2. I would have supposed that a link this strong to already incredibly well established mathematics with a relatively sturdy structure would make logic even easier to analyze than it currently is.
What makes OR the more common connective despite this? Tradition? Ease of formulation of statments in canonical form?
 A: Here is my anecdotal evidence: when dealing with logic in practice, you usually need either AND or OR, but not XOR. I've programmed hundreds, if not thousands of if-tests, many of them testing several statements with connectives. The number of times I really needed XOR could probably be counted on a hand or two.
So my guess is that we humans are, if not inherently better at understanding AND and OR, at the very least more experienced.
A: When you design logic circuits, you usually start with some specification of desired functionality, and then use any number of techniques to capture that with a logical expression.  Those techniques often rely on useful logical equivalences so that you can, for example, use boolean algebra to rewrite and simplify expressions. 
And, as it turns out, the AND and the OR are each other's dual operators, which means that not only is it true that you often find yourself going back and forth between them (think Demorgans's Laws!), but they share lots of logical properties, like Commutation, Association, Distribution, Absorption, Reduction, Idempotence, Adjacency, etc.  Whereas if you were to work with an AND and an XOR, you would need to remember a different set of such logical properties for each of them. In fact, just the very fact that many of these logical principles just mentioned involve both the AND and the OR is a point in favor of using AND and OR as your 'basic' operators, whereas I doubt you would find just as many useful principles involving the AND and the XOR.
