Union or Intersection for f(x)=0 When x in A and B

[evinda]

Hello! (Wave)

When we have: $f(x)=0, \forall x \in A \wedge f(x)=0, \forall x \in B$, do we conclude that $f(x)=0, \forall x \in A \cap B$ or $f(x)=0, \forall x \in A \cup B$? (Thinking)

 

[Evgeny.Makarov]

Don't put a comma between $f(x)=0$ and $\forall x\in A$. Similarly, don't put a comma before "that".

If something holds for all $x\in A$ and all $x\in B$, then it holds for all $x\in A\cup B$.

 

[evinda]

Don't put a comma between $f(x)=0$ and $\forall x\in A$. Similarly, don't put a comma before "that".

If something holds for all $x\in A$ and all $x\in B$, then it holds for all $x\in A\cup B$.

I see... Thank you very much! (Smile)