Truth Table Logic XOR

Question

I'm not sure if my solution is correct. Would be very happy if you can check and say what I did wrong.

a) Is to make A xor B with only conjunction, disjunction and negation. b) Is to check if A xor (B AND C) is equal to ((A xor B) AND (A xor C))

Answer 1

a) No, your last substitution is wrong.

b) By reasoning: if $B$ and $C$ are equal, then both expressions reduce to $A\text{ xor }B$; but if they are different, the expressions reduce to $A\text{ xor }\text{false}$ and $\text{false}$.

Answer 2

In part (a), you made a mistake converting $\lnot (A \land B)$ to $\lnot A \land \lnot B$, double check your demorgans. Similarly, a mistake changing $\lnot (\lnot A \land \lnot B)$ to $A \land B$

The correct use of demorgan's is:

$\lnot (A \land B)$ is equal to $\lnot A \lor \lnot B$

and (try to figure these out on your own before looking at the solution)

$\lnot (\lnot A \land \lnot B)$ is equal to $A \lor B$

For part (b), I looked over it and didn't see any mistakes.