flawed argument

Represent red green color blindness as RGCB; represent cannot distinguish green from brown as ~GB General Principle: RGCB => ~GB, Then contrapositive is GB => ~RGCB The premise is ~GB, ie, it is given that ~GB. The question is whether you can infer RGCB. Symbolically, the question is: is it true that ~GB => RGCB? Note that the statement in question (~GB => RGCB) is a reversal of the positive statement, above, (RGCB => ~GB). Recall that one can never just reverse, which is what the statement in question does - it reverses. So the statement in question, ~GB => RGCB is flawed, because it reverse the positive statement, which, without also negating, is illegal, ie., flawed. Abstractly, If carrots are not hamburgers, and x is not hamburger, then you cannot conclude that x is a carrot. It might be a potato. Hope this helps

@Lauren, Great question. Here's how we diagram the stimulus: RGCB - >can't distinguish between green and brown Gerald can't distinguish between green and brown (satisfies the necessary condition of the above statement) Conclusion: Gerald is RGCB (the sufficient condition of the above statement) The problem with this argument is that it's invoking the necessary condition to conclude the sufficient condition. This is improper logic. If the necessary condition is satisfied, the sufficient condition may or may not be true. If, on the other hand, this argument had said that Gerald CAN distinguish between green and brown (that is, he fails the necessary condition), then we could conclude that Gerald is not RGCB (the sufficient condition is failed). Think about this example argument: All girls in the WNBA play basketball. Alexa plays basketball. Therefore, Alexis is in the WNBA. Do you see how this matches the flaw of the argument in the stimulus? WNBA - >basketball Alexa plays basketball Therefore, Alexa is in the WNBA See how that doesn't make any sense? The necessary condition is being invoked to conclude the sufficient condition. This is precisely the flaw we see in (B). Sinusitis - >lose sense of smell Mary has lost sense of smell (satisfies necessary condition) Conclusion: Mary has sinusitis (sufficient condition is triggered) Just as seen in the stimulus and our sample argument, (B) is incorrectly invoking the necessary condition to conclude the sufficient condition. Does this make sense? Let us know if you have any other questions!