Parity of sum of other elements
Jelly, 3 bytes

+SḂ


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How it works

+SḂ  Main link. Argument: A (array)

 S   Compute the sum of A.
+    Add the sum to each element of A.
     Using _ (subtraction) or ^ (bitwise XOR) would also work.
  Ḃ  Bit; compute the parity of each resulting integer.