鶏 and 卵: the layer and the egg
Distinguish chickens from eggs and read counts, actors, and completed cooking actions.
A chicken's action
鶏, read にわとり, means chicken. 庭で鶏が鳴いています。 says that a chicken is calling in the yard.
鶏が卵を産みました。 says that a chicken laid an egg or eggs. 鶏 before が is the actor, and 卵 before を is the object.
Counting eggs
卵, read たまご, means egg. 卵を六個買いました。 means buying six eggs.
卵が一つ割れました。 says that one egg broke. It does not identify anyone deliberately breaking it.
Animal counts and egg counts
鶏が二羽いて、卵が三個あります。 gives two chickens and three eggs. Distinguish 羽 for the birds from 個 for the eggs.
卵をゆでましたが、まだ食べていません。 says that the eggs were boiled but have not been eaten yet. Cooking and eating have different completion states.
What laid the eggs in 鶏が卵を産みました?
Show the answer and why
The chicken. 鶏が identifies the actor.