any expert could help me why this sentence is True?

if L ∈ NP and L ≤

_{p}3−SAT (i.e: reduce L to 3-SAT in poly time) then L is NP-Complete.

Answer:

This statement is false. Since 3SAT is NP-complete, *every* problem in NP polynomial-time reduces to 3SAT, so if you choose *any* language in NP, then it will polynomial-time reduce to 3SAT. In particular, if you choose the empty language ∅, which is known not to be NP-complete, then ∅ ∈ NP and ∅ reduces toe 3SAT, but ∅ isn't NP-complete.

Hope this helps!

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