Law of Syllogisms

You most likely use the Law of Syllogisms on a daily basis.  The general idea of it is used in a Direct TV commercial.  Just replace every time the narrator says “when” with “if,” and you have yourself a whole list of conditional statements that lead us from the hypothesis of “a cable company puts you on hold” to a final conclusion of “ending up in a roadside ditch.”

watch the video here:

DIRECTV – Don’t Wake Up in a Roadside Ditch 2012 Commercial

More formally, the Law of Syllogisms states:

If p–> q and q–> r are true statements, then p–> r is a true statement.

Let’s break this down:

p–> can be represented with the familiar diagram:

q–> r can be represented as a Venn Diagram too:

But you know something more about that “q part of the above diagram!  You know that there is a 3rd circle contained in “q” that has all of the events that fall under p.  So altogether, p–> q and q–> r give us:

And from this, we can see if an event meets the conditions of statement “p“, that it also means that r is true as well!  That’s the Law of Syllogisms!


Consider the two conditional statements: If your cable company puts you on hold, then you get bored.  If you get bored, then you eat all of your Doritos.

Assuming these statements are true, if we know that your cable company put you on hold, we can jump to the conclusion that you ate all of your Doritos.

Try making a Venn Diagram that represents these ideas.  Then get some more practice with them on a Khan Academy module here.

*Warning*: Make sure that you’ve also taken a look at the post on Law of Detachment.

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4 Responses to Law of Syllogisms

  1. taran meek says:

    i was really intrigued by these syllogisms and i cant wait to learn more!!!!

    • taran meek says:

      hey come to my football game 2night. i think if i use the law of syllogisms corectly i will be able to be an all star player. if you come to my game, then i will be happy. there can multiple ways that i am happy but if you come to my my game i will be happy

  2. Alex Gayraud says:

    i really love this class and i was wondering if i could get private lessons? 🙂

  3. Robert Thomas says:


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