Some and Most Diagramming Drill

[jailenea]

Can someone please explain the following? I am looking at page 433 ("Some and Most Diagramming Drill") of the Logical Reasoning 2020 Digital Edition book.

Prior to this drill, the "relationships involving Some" subsection on page 429 introduced double arrows for "some" statements. How are these to be read since they're double ended? I assumed from both left to right and right to left. However, that only makes sense (at least for me as of now) in certain instances.

For example - back to the drill on page 433:

#1: At least one heron has blue feathers
The correct answer is H <-some-> BF. I read this as both "some herons have blue feathers" from left to right & "some blue feathered birds are herons" from right to left. Is this correct?

Now let's take #3: Not all of the Smallville roads are safe
The correct answer is SR <-some-> ~safe. I read this as both "some Smallville roads are not safe" from left to right and "some not safe roads are Smallville roads" from right to left. This doesn't sound right. Is it correct?

This gets even more confusing with #4: A few of the schools no longer offer business degrees
The correct answer is S <-some-> ~OBD. I read this as both "some schools no longer offer business degrees" from left to right. Again, the right to left one is the weird sounding one, which I read as "some non business degree offering schools are some schools." This one truly doesn't make sense to me.

Am I reading them wrong? Misunderstanding something? Why are they all double arrowed? Are they only meant to be read both ways if there are no negative symbols on either end? What's going on?

[Robert Carroll]

jailenea,

All "some" statements are reversible by definition.

In your first situation, you could read it two ways:

"Some herons have blue feathers"

or

"Some things with blue feathers are herons"

Note that we don't want to add "birds" to the statement if it's not already there. Because all herons are birds, it won't alter the truth of the statement, but it doesn't count as a translation of the statement if new things are added when changing the direction.

Similar considerations apply to #3:

"Some Smallville roads are not safe"

or

"Some things that aren't safe are Smallville roads"

It's possible that it's sounding awkward to you because you're adding the superfluous "roads" to both statements, instead of keeping it on one side.

#4 has similar issues, and you've added a second "some" to the right-to-left reading. Instead:

"Some schools no longer offer business degrees"

or

"Some things that no longer offer business degrees are schools"

Hope this helps!

Robert Carroll