Seven Commandments as a subset of the Ten Commandments
Defining the the Seven Noahide Commandments as a subset of the Ten Commandments, may be an useful analogy to explain the Seven Laws to those who accept the "Ten Commandments" but view the Seven Noahide Law as a Rabbinic innovation.
It is plausible that the first, fourth and fifth commandments only apply to the Children of Israel. The first commandment declares that the four letter Name of G-d was given to the Children of Israel when they left Egypt. The fourth commandment, keeping the Sabbath, is almost universally recognized as applying only to the Children of Israel. The fifth commandment may imply that the commandment of maintaining the Massorah, the Oral Tradition, from Father to Son, Teacher to Student is only obligatory on the Jewish people.
|I am the Lord your God||1|
|You shall have no other gods before me
You shall not make for yourself an idol
|You shall not make wrongful use of the name of your God||3||2
|Remember the Sabbath and keep it holy||4|
|Honor your father and mother||5|
|You shall not murder||6||3
|You shall not commit adultery||7||4
|You shall not steal||8||5
|You shall not bear false witness against your neighbor||9||7
|You shall not covet your neighbor's wife
You shall not covet anything that belongs to your neighbor
* The sixth Noahide commandment is "The Prohibition of flesh from a Living Animal". Rabban Gamliel extends this to Blood. But it is important to note that all seven commandments were originally given to Adam. Adam was forbidden to eat meat: "Rab Judah said in Rab's name: Adam was not permitted to eat flesh, for it is written, [Behold I have given you all the herbs, etc.] to you it shall be for food, and to all the beasts of the earth (Gen. 1:29)" - Sanhedrin 59b.
Thus it is possible that the meaning of this commandment is more general than just the limb of a living animal. Rabbi Dr. Freedmen in the Soncino Talmud says "By interpreting thus: Thou mayest eat that which is now ready for eating, but not whilst the animal is alive. It is perhaps remarkable that a verse, the literal meaning of which is obviously permission to enjoy, should be interpreted as a series of prohibitions. Yet it is quite in keeping with the character of the Talmud: freedom to enjoy must be limited by moral and social considerations, and indeed only attains its highest value when so limited. Cf. Pirkei Avot 6:2: No man is free but he who labours in the Torah."