[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.

Step 5 – Find the contrapositive

Step 6 – Translate back to English

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

Just like that! Now try these:

No ice cream will be served.
i/s
s/i
Classics never get old.
C/o
o/C
Carrots cannot grow in the winter.
g/w
w/g
The car cannot fit both the cat and the dog.
c/d
d/c
No dog is funny.
d/f
f/d
You cannot fight crime and run marathons.
f/r
r/f
None of the girls were angry.
g/a
a/g
Recycled materials never pollute the water.
R/p
p/R

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