Another method of deriving Torah laws is the concept of Kal Vachomer. This is a type of logic known as a fortiori reasoning. If something light is true, then it would certainly apply to the more severe.
An example of קל וחומר would be that if something was forbidden on Yom Tov, it would certainly be forbidden on Shabbat. This is because, the penalty connected to Shabbat violation is more severe than Yom Tov violation.
A more complex Kal Vachomer would be how it is learned that a Kohein may not marry a Jewish girl who had relations with a non-Jew.
The reasoning is as follows: at the time of the Torah, a daughter of a Kohein who had such relations, was disqualified for life, for ever being allowed to eat the sanctified food designated for Kohanim, known as Teruma.
A daughter of a Kohein, who was married to a non-Kohein, is not allowed to eat Teruma, as long as she is married. If she is childless and divorced, she may go back to her father’s house, and eat Teruma again. However, since she is a divorcee, she may not ever marry a Kohein, as a Kohein is forbidden to a divorcee.
The קל וחומר would then be, that if a divorcee, the daughter of a Kohein, who is allowed to eat Teruma, but is not allowed to marry a Kohein, then certainly (קל וחומר) a daughter of a Kohein who is disqualified from eating Teruma, may not marry a Kohein.
Two examples were thus given as to what Kal Vachomer means. One example was light, and one was more heavy, or complex.