Lesson 2 Questions

[Stephanie Oswalt]

We recently had some questions from a student regarding the content in Lesson 2. Below are the questions and the instructor's response.

Conditional Language:

I am having trouble with how Jay D. was able to manipulate the first passage and use the contrapositive? Is the contrapositive something we can always use to be able to get for example an "A-->B and B-->C (A-->C)? as shown on the 2nd pic compared to the first pic diagramming the rules from what we had from the passage.

Then in all that mess how we got to the answer E which makes sense because of the rulles drawn but how to use the contrapositive and when to able to get to this answer is where I got tripped up.


THEN the other question was about the "UNLESS" Equation and Power words. When exactly would I be using these shortcuts or equations? When the word "unless" is in the passage?

Edgar

Thanks for the question, Edgar! It may help to remember that a contrapositive means exactly the same thing as the conditional claim that you started with. They aren't two different things, but two different ways of saying the same thing. Consider these examples:

If I go in that haunted house, you have to go with me.
I will not go in that haunted house unless you go with me.
If you won't go with me, I will not go into that haunted house.

These all mean the same thing, and can be expressed either as:

I Go HH -> You Go HH

or

You Don't Go HH -> I Don't Go HH

So the answer is yes, you can always use the contrapositive of a conditional relationship to help connect common terms, as happened in this question with "willing to compromise/unwilling to compromise," because you are not changing any of the information but just changing the way you represent that information. When you see that you can manipulate the terms to find a common term, do that, because it is in those connections that the answers will be found.

As to the power words that trigger the use of the Unless Equation, there are four of them: Unless, Except, Until, and Without. When you see any of those, they indicate a Necessary Condition, and that belongs on the right side of your conditional arrow. The other condition in that relationship gets negated, and that negated condition becomes the Sufficient Condition. In my second example above, that's what happened - "unless" refers to you going in the haunted house with me, and "I will not go" was negated to become "If I go." That's the first version of the diagram that I provided.

Practice that use of Unless/Except/Until/Without until it becomes second nature, because you will certainly need it at some point in your test!

-Adam