Does Elayne know who Rand’s father is and that he killed her grandfather Laman?
It is not confirmed that Janduin killed Laman.
Do Aviendha or Rand know that Laman was Elayne’s grandfather (re: the sword that Aviendha gave to Rand to discharge her toh )?
Aviendha probably didn’t know but Rand definitely did.
ETA—these topics were to be included in possible prequels.
The reply is correct that it has not been confirmed that Janduin killed Laman. However, Laman was not Elayne’s grandfather since Laman died childless [NS5].
laman ,
rand ,
elayne ,
aiel war ,
janduin ,
prequels
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