The gemara says that an egg inside a trayfa mother is trayfa because it comes from only one source. But if the hen mated there is a second source (the rooster) which permits.
Didn't we learn (in Beitza) that we can always assume the hen has mated with a rooster (Because it will cross rivers and travel many miles to secretly find the hen)
Randy Lazarus, Mitzpe Yericho, Israel
The Gemara in Beitzah (end of 7a) teaches that sometimes the egg is "Safna me'Ar'a": the hen lays an egg without the presence of a male. Ravina there says that we know that whenever there is a male with her, she does not lay an egg without the male. The Gemara (beginning of 7b) then says that if there is no male within the distance of 60 houses, the egg may have been "Safna me'Ar'a" and laid without any involvement of the male. The Gemara there also states that if there is a river between the female and the male, the female will not cross it to reach the rooster unless there is a bridge over the river.
In short, the Gemara in Beitzah does not say that we can always assume that the hen mated with a rooster. This is why the Gemara here in Chulin says that if the egg is "Safna me'Ar'a," it comes from only one source, and in such a case the egg inside a Tereifah mother is also Tereifah.
Shanah Tovah,
D. Bloom
Rebbe,
Aynenu ro os, our eyes see, that there is an entire industry of battery eggs, which are Safna me'Ar'a. There are probably millions of sterile unfertilized eggs layed every day which are produced, washed and processed at large industrialized farms. Those farms have chicken coops which do have roosters and produce fertilized eggs and separate facilities where they successfully keep the roosters away from the hens so they can lay fertilized eggs for the market.
So we see that we can keep roosters away from hens when needed.
Sam Kosofsky
I assume that the industrial farms make special precautions to ensure that the roosters cannot reach the hens, because the industry is concerned that these hens should lay only unfertilized eggs. No doubt that the hens are in cages. In such conditions, the Gemara in Beitzah would agree that there is no worry that they might have mated.
(Of course, there are Halachic differences between eggs which are Safna me'Ar'a and between free-range eggs with respect to bloodspots found in the eggs.)
Kol Tuv,
Dovid Bloom