Is xor operator ie(+) distributive over union ? also over intersection?

let us take two sets A and B and A={0,1},B={0,1} as the sets are binary.

now another set C={0,1}

we know For any sets A, B, and C, the following identities hold

distributive laws:

A union (B intersection C)=(A union B) intersection (B union C)

A intersection(B union C)=(A intersection B) union (B intersection C )

Now for A,B,C union=intersection={0,1}

For xor logic A xor B=A'B+AB' so our aim is to find whether xor is distributive or not

So we got to prove:

is A xor (B xor C)= (A xor B) xor (B xor C) correct or not?

Now please proceed

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