Problem 89 (difficulty: 3/10)

Let \(\displaystyle A\Delta B=(A\setminus B)\cup (B\setminus A)\) denote the symmetric difference of the sets \(\displaystyle A\) and \(\displaystyle B\). Show that for any sets \(\displaystyle A,B,C\):

 (1)  \(\displaystyle A\Delta \emptyset=A\),     (2)  \(\displaystyle A\Delta A=\emptyset\),     (3)  \(\displaystyle (A\Delta B)\Delta C=A\Delta(B\Delta C)\).

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