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joaquin-acuna on March 3, 2020

diagramming - example 6

in example six for the sufficient and necessary video lesson, I notice that when diagramming the premises, the contrapositives for each premise were not stated. Is there any reason why? in other words, when is it convenient to state the contrapositives and when it is not?

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SamA on March 4, 2020

Hello @joaquin-acuna,

While you are first getting familiar with conditional reasoning, it is always a good idea to write the contrapositives. Eventually, you will understand the sufficient/necessary relationship well enough that you don't always have to write the contrapositive down. I now write them only when I feel like it is going to help me. Here is a missing conclusion drill for example:

P: X - - - - >Y
P: Z - - - - > not Y

As it is written, it is not so easy to see that "Y" is the common term between the two premises. So, I will take the contrapositive of the second premise.
Y - - - - -> not Z
Now I have a way to connect my premises with Y.
X - - - - -> Y - - - - -> not Z

Conclusion: X - - - - -> not Z

In example 6 from the lesson, it is not necessary to take this step. The premises are written in a way that they already form a chain of reasoning. Remember that a contrapositive carries the exact same logic as its positive statement. They have the same meaning. Continue to practice, and you will start to understand when they are useful.

joaquin-acuna on March 6, 2020

understood, thank you very much.

Ravi on March 20, 2020

@joaquin-acuna, let us know if you have any other questions!