[This is a lesson excerpt from our online course, for which we invite you to enroll.]

Group 4 is made up of the following terms:

  • No
  • None
  • Not both
  • Never
  • Cannot

All the words in this group follow this translation rule:

You pick either idea, then negate that idea, then make the idea you negated the necessary condition.

Let’s try it, in six simple steps:

None of the Americans attended the dictators’ party.

Step 1 - Identify the logical operator

Here, it’s “none.”

Step 2 - Identify the two main concepts (or groups, categories, events or ideas)

Here, it’s the two events “being an American” and “attending the dictator’s party.”

Step 3 - Assign symbols to the two main concepts

Here, “A” for “being an American” and “ADP” for “attending the dictator’s party.”

Step 4 - Apply the translation rule

Here, pick an idea “A”, negate it to “/A”, and make "/A" the necessary condition.

ADP –> /A

Step 5 - Find the contrapositive

A –> /ADP

Step 6 - Translate back to English

If you’re an American, then you did not attend the dictator’s party.

Just like that!

(Photo credit: purpleslog - http://www.flickr.com/photos/purpleslog/)