SUBSET-SUM = {S, t there exists S' S
N such that
= t N},

N = set of natural numbers

**Theorem 34.15: SUBSET-SUM **** NPC**

Proof:

- 1.
- SUBSET-SUM NP. Just add up elements of S' and compare sum to t.
- 2.
- L' = 3-CNF-SAT
- 3.
- 3-CNF-SAT SUBSET-SUM
- 4.
- x
3-CNF-SAT
f(x)
SS

Proof is complex.

Alternate proof: Reduce from VERTEX-COVER (1st edition).