Sp. Relativity: supernova explosion

[hy23]

Homework Statement

Star D goes supernova at x=0 and t=0. One year later and 2 ly away (measured by astronomers in the galaxy), star E explodes. The explosions are observed by 3 spaceships going from D to E at respective velocities:
v₁=0.3c
v₂=0.5c
v₃=0.7c

What are the times of the two explosions as measured by scientists on each of the 3 spaceships?
Does one spaceship find the explosions to be simultaneous? Does this violate causality?
Does one spaceship find that E explodes before D? Does this violate causality?

Homework Equations

Not sure whether or not to use the spacetime interval or Lorentz transformations
s²=c²t²-x²
x'=$$\gamma$$(x-vt)
t'=$$\gamma$$(t-vx/c²)
where $$\gamma$$= t/t'
where t' is proper time. ( I hope I have this right at least)

The Attempt at a Solution

I haven't done the calculations yet because I have no idea which equation to plug my values into, but just looking at it qualitatively, isn't the time that D explodes always going to be t=0 for all 3 spaceships?
And the spaceships traveling faster will find that E explodes earlier?

 

[BigJDubs]

Would this not violate causality? Since the explosions were simultaneous according to people in the galaxy, the time that E explodes before D would be different for each of the 3 spaceships, so wouldn't causality be violated?