Shabbat 86 - Three days before the giving of the Torah
Next in the list of "from where do we know" is "From where do we know that a woman who emits semen on the third day after an intercourse becomes ritually impure?" - From the Torah phrase, "Moses said to the people, 'Keep yourself in readiness for three days. Do not come near a woman.'"
The Torah had to be given to people who are ritually pure. All other sources of impurity can be eliminated by going to a mikveh, after which the person becomes ritually pure. Therefore, the only reason for the three-day waiting period was the potential for semen - if it is viable - to be expelled later, and the semen is considered viable for three days. The Talmud also discusses other opinions on how long this period can be.
Actually, a person right out of the mikveh is considered pure, with a tinge of impurity until sunset. Still, it could have been enough for giving the Torah. Why, for example, was the Torah not given on Friday, right after everyone went to a mikveh? - Because God did not want to do it in secret at night. Then why was the mikveh time not set for Saturday morning, with the Torah given right after that? - Because then some would be returning from the mikveh, with others just going there, and the Jewish people needed a complete unity.
Art: German School - Purity