Set theory problem

Let A A , B B , C C and Y Y be subsets of X X and define the application f Y : P ( X ) P ( X ) { f }_{ Y }:P(X)\longrightarrow P(X) given by f Y ( A ) = A Y = ( A Y ) ( A Y ) { f }_{ Y }(A)=A△Y=(A∪Y)∖(A∩Y) , where P ( X ) P(X) denotes the power set of X X . Which of the following statements hold true?

  1. The application is bijective
  2. ( A B ) C = A ( B C ) (A△B)△C=A△(B△C)
  3. f A f B = f B f A { f }_{ A }\circ { f }_{ B }={ f }_{ B }\circ { f }_{ A }
  4. The application is not surjective
1, 2 and 3 2 1 1 and 3 3 3 and 4 1 and 2 4

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