#24 - Biologist: We know the following things about plant X. Specimens with fuzzy seeds always have

[Administrator]

Complete Question Explanation

Must Be True. The correct answer choice is (C).

Answer choice (A):

Answer choice (B):

Answer choice (C): This is the correct answer choice.

Answer choice (D):

Answer choice (E):

This explanation is still in progress. Please post any questions below!

[Mmjd12]

I struggled to diagram this one because I was unsure which was the necessary and sufficient conditions.

I did:

Fuzzy Seed Long Stem + White Flower


Curly Leaves White Flower

Thorny Seed Pods Curly Leaves

I guess with (C) being correct answer that I switched the necessary and sufficient conditions?

[Jeff Wren]

Hi Mmjd12,

The good news is that your diagrams are all correct!

Where you may have made a mistake is either not diagramming the contrapositives of these conditional statements (which you definitely want to do), incorrectly diagramming them, or not properly linking the statements/contrapositives.

While it's a good idea to diagram all of the contrapositives, the one that we're actually going to use to solve the question is the contrapositive of the first conditional statement.

Fuzzy Seeds --> Long Stem + Not White Flowers

To take the contrapositive of this statement, you reverse and negate all of the terms. In addition, the word "and" (shown as the + sign in the diagram) becomes the word "or."

So the contrapositive is:

Not Long Stem or White Flowers --> Not Fuzzy Seeds

(Notice that since this contrapositive has an "or" in the sufficient, the term "White Flowers" by itself is sufficient to guarantee Not Fuzzy Seeds.)

Linking the other statements to this contrapositive gives us the following long chain:

Thorny Seed Pods --> Curly Leaves --> White Flowers --> Not Fuzzy Seeds

The stimulus tells us that the particular specimen has a Long Stem and Curly Leaves.

The Long Stem term doesn't trigger anything, so you can basically not worry about it.

Using the above chain, starting at the Curly Leaves term and following the arrows to the right, this tells us that the specimen has White Flowers and Not Fuzzy Seeds, which is perfectly described in Answer C.

Notice that the Thorny Seed Pods term is "to the left of" the Curly Leaves term in the diagram, meaning that we do not know anything about whether the specimen has Thorny Seed Pods. (Don't make a Mistaken Reversal and try to go backwards against the arrow from Curly Leaves to Thorny Seed Pods.) Several wrong answers (A,B, D) mention Thorny Seed Pods, and we do not know whether or not the specimen has them.