Another way of show number of exclusive elements in a set Sorry for any confusing. This is the first time I asked on this site, if there is any term that's wrongly used, please let me know

So given a diagram of A and B, to show exclusively A and exlusively B, we have

A or B - A and B


alternatively, we have

~ (A and B)


Then given A, B, C. To show exlusively A,exlusively B and exlusively C, we can do

A or B or C - A and B and C - A and B and not C - A and C and not B - B and C and not A


or 

~ (A and B and C) - A and B and ~C - A and C and ~B - B and C and ~A

Then given A, B, C and D, we have 

A or B or C or D - A and B and C and ~ D - A and B and D ~ C - A and D and C and ~ B - B and C and D and ~ A - A and B and ~ (C and D) - A and C and ~ (B and D) - A and D and ~ (B and C) - B and C and ~ (C and A) - C and D ~ (A and B)


I came up with above expression by drawing the van diagram. Is the above expression correct? Is there a better way to express this?
There is the operator xor which has the following truth table 

Its symbol is $\oplus$, so in general if you have $A_1, A_2, A_3,....,A_n$ , a good expression is :

$$A_1 \oplus A_2 \oplus . . . \oplus A_n $$

:)
There is the operator xor which has the following truth table 

Its symbol is $\oplus$, so in general if you have $A_1, A_2, A_3,....,A_n$ , a good expression is :

$$A_1 \oplus A_2 \oplus . . . \oplus A_n $$

:)