NP Complete Proof - Polynomial Reduction We know that the INDEPENDENT-SET problem is NP Complete i.e $\langle G',k'\rangle$ means graph $G'$ has an Independent set of size $k'$. I am preparing for the finals an a sample question is to prove TRIANGLE-FREE-SET to be NP Complete. 
$$TRIANGLE-FREE-SET:=\{\langle G,k\rangle| \text{$G$ has a subset of vertices of size $k$ whose induced subgraph is triangle free}\}$$

To give a polynomial reduction of IS instance $\langle G',k'\rangle$ to TFS, I thought of adding an extra vertex and connecting this extra vertex to all the original vertex of the IS problem instance and then have $k=k'+1$. However, I am stuck trying to prove that if $\langle G,k\rangle \in TFS$ then $\langle G',k'\rangle \in IS$. Any leads appreciated.
Probably you can get your answer from here: Reducing independent set to triangle-free subgraph
Basically in order to prove that $TFS$ is NP-complete you can just check the first proof in the link's answer. Given a graph $G$ with an independent set $k$, there exists a $G'$ with a $TFS$ of size $|V|+k+1$.