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# Contrapositives and Denying the Necessary Condition

Alum Member
edited January 2015 in General 41 karma
Can anyone point me to a lesson that explains when contrapositives should be utilized and when it should be ignored?
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• Alum Member
166 karma
Lesson 11 and 12 of Introduction to Logic.

i dont recall specifically if a point was made regarding ignoring contrapositives...and your question leads me to think you may be mixing up somethings.

the Contrapositive is the exact same thing as the positive version of the argument, that is, they are interchangeable and exactly the same. you just use whichever version is more convenient to use. (Convenient meaning that there are times when you would link strings of rules together and some may involve both positive and negative components of the same item, so you use whichever version that can easily fit in your string)

Example
A--->B means that if I have A, then i must have B.
The contrapositive of that is
/B-->/A meaning that if i dont have B, then i cannot have A

Both statements have the same meaning and value, they are just written differently.

Now, if i have that same argument
A--->B and the reality is that i have a B, that does not mean I have to have an A. The rule just becomes irrelevant and you can ignore it.

Additionally, if I dont have an A, well, i dont have to have a B, again, the rule becomes irrelevant and can be ignored.
• Alum Member
41 karma
Thanks, LSATCommitted, I may not have framed my question in the best. I will revisit the lesson and see I still need clarification.
• Alum Member
41 karma
FYI: I was confusing terminology. Below is the clarification I was after:

CONDITIONAL RULES Trigger v Irrelevant

Sufficient satisfied Rule triggers, necessary must be satisfied.
Sufficient failed Rule irrelevant, necessary free to satisfy or fail.
Necessary failed Rule triggers, sufficient must be failed.
Necessary satisfied Rule irrelevant, sufficient free to satisfy or fail.