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

Group 3 is made up of the following terms:

• Unless
• Until
• Or
• Without

These are my favorites, because they’re notoriously confusing for students. I’m not sadistic or anything. That’s not why I like them. I like them because of how easily this apparent difficulty can be overcome by sticking to your translation mechanism.

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 sufficient condition.

Let’s try it:

Don’t go to Hawaii, unless you want to have a good time.

Step 1 - Identify the logical operator

Here, it’s “unless.”

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

Here, it’s the two events “not going to Hawaii” and “having a good time.”

Step 3 - Assign symbols to the two main concepts

Here, “/H” for “not going to Hawaii” and “GT” for “having a good time.”

Step 4 - Apply the translation rule

Here, pick an idea - “/H” - and negate it - “H” - and make it the sufficient condition.

H –> GT

Step 5 - Find the contrapositive

/GT –> /H

Step 6 - Translate back to English

If you don’t want to have a good time, then don’t go to Hawaii.

All done!

The thing about this group is that it indicates necessity, doesn’t it? Unless is emphasizing the necessity of what comes after it. But then it’s simultaneously warning you about the consequences of not following through with that necessity. So, with “Don’t go to Hawaii, unless you want to have a good time,” the “unless” is indicating that “wanting to have a good time” is the necessary condition. Okay, but it’s the necessary condition for what? Well, the sentence doesn’t explicitly say. It’s implied that it’s the necessary condition of “going to Hawaii.” Is that too confusing? Then just straight forwardly follow the translation mechanism and you’ll be golden.

(Photo credit: paul bica - http://www.flickr.com/photos/dexxus/)