MHB Is the Symmetric Difference Problem Solved?

[Yankel]

Hello all,

For each of the following statements, I need to say if it is true or not, to prove if it is true or to contradict if not.

1)
\[A\bigtriangleup (B\cap C)=(A\bigtriangleup B)\cap (A\bigtriangleup C)\]

2)
\[A\cup (B\bigtriangleup C)=(A\cup B)\bigtriangleup (A\cup C)\]

Where
\[\bigtriangleup\]

is the symmetric difference.

I do know that:

\[A\bigtriangleup B=(A-B)\cup (B-A)\]

which is:

\[(A\cap B^{C})\cup (B\cap A^{C})\]How do I proceed from here?

Thank you !

 

[Evgeny.Makarov]

Both equations can be refuted by taking $A$ to be the universal set.

 

[Yankel]

Is it correct that these are the corresponding Venn diagrams of both sides in the first statement?
(assuming your way, of making A universal).

View attachment 6444