When a result is statistically significant, does it depend on the value of beta?

#1
I would need to get help to motivate the right statement (the three below):

- When a result is statistically significant at α = 0.05, this is also significant at α = 0.01.

- When a result is statistically significant at α = 0.01, this is also significant at α = 0.05.

- The result depends on the value of beta.

I am pretty sure that the second statement is right, that when α= 0.01 is significant, then would 0.05 also be that, and not vice versa. But can anyone explain the third statement, does the result depends on the value of beta? Yes or no, and why? I guess it does not, but I don't know how I can motivate/explain this?

I would be grateful if anyone wants to help.

Best,
L.