Is it a sum-free set?

Python 2, 41 bytes

lambda s:s==s-{a+b for a in s for b in s}

s should be a Python set.

Fun fact: sum-free is an anagram of my name.

Jelly, 5 bytes

ṗ3ḅ-P

Try it online!

How it works

ṗ3ḅ-P  Main link. Argument: A (array)

ṗ3     Take the third Cartesian power of A, i.e., generate all triplets that
       consist of elements of A.
  ḅ-   Convert each triplet from base -1 to integer.
       This maps [a, b, c] to a - b + c = (a + c) - b.
       If (a + c) belong to A, this will yield 0 for some b.
    P  Take the product of all resulting integers. 

Pyth - 8 5 bytes

Thanks to @FryAmTheEggman for saving me 3 bytes.

!@sM*

Test Suite.

!             Logical not. This makes the empty intersection true and vice versa.
 @    Q       Setwise intersection with input (implictly).
  sM          Map sum to all the pairs.
   *QQ        Get all pairs by doing cartesian product with input*input (implicit).