Sufficient & Necessary Questions - - Question 1

People who are red/green color-blind cannot distinguish between green and brown. Gerald cannot distinguish between gr...

LSATChris September 20, 2019

Missing premise, conclusion, and transitive property

I'm having issues with understanding the properties above.. I'm having issue connecting the dots please help.

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SamA September 23, 2019

Hello @LSATChris,

Your struggle with this question is likely based on a misunderstanding of sufficient and necessary conditions. However, this is a really good question with which to practice those concepts.

Premise: People who are red/green color-blind (RGCB) cannot distinguish between green and brown (DGB.)

RGCB (sufficient) - - - - - - > cannot DGB (necessary)

In order for the sufficient condition to be fulfilled, the necessary condition must be true. If you can distinguish between green and brown, then you are not RGCB. No exceptions.

However, you cannot reverse this statement. If you cannot distinguish between green and brown, are you RGCB? Not necessarily. There could be other causes of not being able to distinguish between green and brown.

This is the mistake that the author makes.

Premise: Gerald cannot distinguish between green and brown.
Conclusion: Gerald is Red/Green Color-Blind.

This is not necessarily true. The author has mixed up her sufficient/necessary conditions.

Let's find an answer choice that makes the same reasoning error.

B Premise: People who are suffering from sinusitis (S) lose their sense of smell (LSS).

If S - - - - -> LSS. No exceptions.

B Premise: Mary has lost her sense of smell.
B Conclusion: Mary has sinusitis.

This is the exact same mistake that the author of the passage made.
LSS - - - - - > S is a mistaken reversal.

There may be other causes of a lost sense of smell, so we cannot say for certain that Mary has sinusitis. Just as we cannot be certain that Gerald is red/green color-blind.