A $XOR$ $K$ is given. Both $A$ and $K$ are unknowns.
Can the value of $K$ be guessed? Can the values of $K$ can be deduced if the size of $A$ & $K$ are known? What is the smallest set on which bruteforcing can be performed to get the value of $K$?
Pardon if I was unclear.
I have the following problem
Problem: A ,A xor B , B xor C, C xor K are shared between four people to arrive into the secret K by XORing all the above values together.
In a special case A is not available (the first value). Would any of the participants be able to deduce the value of K in that case?
Assuming you mean sets and symmetric difference $A \Delta K =(A \setminus K) \cup (K \setminus A)$, there is NOTHING that knowing $A \Delta K$ can tell you about $K$ if you don't know anything about $A$. That is because given $K$, you can get ALL the possible results for $A \Delta K$ by varying $A$. (If you want the result $X$, there is exactly one $A$ that will give $A \Delta K = X$, namely $A = X \Delta K$).
The answer is the same if you meant XOR and logical variables (propositions).