Perhaps you are thinking of Lot? The incestuous relationship between Lot and his daughters occurred more than 400 years before Noah was given the law, including the laws forbidding incest and polygamy. The only real sin that took place was that Lot failed to provide the opportunity for his daughters to marry.
(If Genesis is to be believed, then we all sprang from incestuous relationships, the children of Adam and Eve had to marry and mate one another.)
>> “The incestuous relationship between Lot and his daughters occurred more than 400 years before Noah was given the law” <<
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You are quite confused.
We do not know when Noah received the law, but we do know that he did receive some law, or else how would he have known what animals were unclean.
Lot lived many generations after Noah died.
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Lot lived after Noah. Noah is Genesis 5. Lot's story begins in Genesis 12, (After his birth is mentioned in Genesis 11.)
Perhaps you mean Moses. But the law did not forbid polygamy either. David and Solomon both had multiple wives and found favor with the Lord for quite a while.
I don't see any reason why Genesis should NOT be believed. Don't forget, these first humans lived hundred of years and we don't know how long they remained in childbearing condition. If you look at cats, for example:
First year: 12
Second year: 66
Third year: 382
Fourth year: 2,201
Fifth year: 12,680
http://www.care2.com/greenliving/how-long-does-it-take-2-cats-to-turn-into-80-million.html/2
Granted, humans aren't cats and they don't have "litters", though we hear of women giving birth to multiples all the time. Plus, a cat's lifespan is 15 - 20 years AT BEST. It's only around 5 for feral cats these days. For humans who lived for hundreds of generations it's not unfeasible that a man might mate with a distant relative and it not BE incest at all.
Well; then... perhaps you can tell us how many UNCLEAN animals Moses placed on the ark?