Basic and Advance C Question:

Answer #1
There seem to be a few missing operators, like ^^, &&=, and ->=.

A logical exclusive-or operator (hypothetically ``^^'') would be nice, but it couldn't possibly have short-circuiting behavior analogous to && and || Similarly, it's not clear how short-circuiting would apply to hypothetical assignment operators &&= and ||=. (It's also not clear how often &&= and ||= would actually be needed.)
Though p = p->next is an extremely common idiom for traversing a linked list, -> is not a binary arithmetic operator. A hypothetical ->= operator therefore wouldn't really fit the pattern of the other assignment operators.
You can write an exclusive-or macro in several ways:
#define XOR(a, b) ((a) && !(b) || !(a) && (b)) /* 1 */
#define XOR(a, b) (!!(a) ^ !!(b)) /* 2 */
#define XOR(a, b) (!!(a) != !!(b)) /* 3 */
#define XOR(a, b) (!(a) ^ !(b)) /* 4 */
#define XOR(a, b) (!(a) != !(b)) /* 5 */
#define XOR(a, b) ((a) ? !(b) : !!(b)) /* 6 */

Answer #2
The first is straight from the definition, but is poor because it may evaluate its arguments multiple times The second and third ``normalize'' their operands to strict 0/1 by negating them twice--the second then applies bitwise exclusive or (to the single remaining bit); the third one implements exclusive-or as !=. The fourth and fifth are based on an elementary identity in Boolean algebra, namely that
_ _ a (+) b = a (+) b

(where (+) is exclusive-or and an overbar indicates negation). Finally, the sixth one, suggested by Lawrence Kirby and Dan Pop, uses the ?: operator to guarantee a sequence point between the two operands, as for && and ||. (There is still no ``short circuiting'' behavior, though, nor can there be.)