I don't know about regulations here. Personally, I think that being open and honest is the best thing (and this is how I handled it). Telling that you have been interviewed for some other positions shows that other committees consider you as a possible candidate which is good for you, especially if you have been interviewed at places with higher prestige. One the other hand, I do not think that a committee will think "Oh this guy has been interviewed there, so we should we hire him...". But probably I am wrong. Moreover, I agree that it does not harm to say that you do not want to disclose your other interviews.

Should I tell other interviewers where else I've interviewed?
Give a formal proof for the claim that the set $\{xor\}$ is not functional complete.

One possible way is to show that we cannot create the function $\lnot$. I tried to prove it by using induction on the structure of $A$. If $A$ is a formula and $V$ is a model that gives $f$ to all atomic formulas then $V(A) = f$. The base case is $A = p$ and so $V(A) = f$. We assume that it holds for the formulas $B$ and $C$. We have $A = xor(B,C)$ and by using the induction hypothesis and the definition of $xor$ we get $V(A) = f$.

But I want to show that we cannot create the function $\land$ I tried using the same method as before but it doesn't seem to work. What should the induction hypothesis be in this case?
