### Formal Logic Additive Inference Drill Question

Posted:

**Wed Jul 12, 2017 10:19 pm**Hi,

I was working on the formal logic additive inference drills found on page 334 of the 2013 edition of the Logical Reasoning Bible. While doing the questions I ended up "discovering" some inferences that were not in the answer key and I would like some clarification.

1)

Some A's are B's

No B's are C's

All C's are D's

Initial diagram: A B C D

The answer keys lists the inferences as:

A notC

D notB

My question is: Why isn't A D a valid additive inference as well? Can we not recycle A notC D and ride the some-train to my answer?

Also, for question 2:

2)

All X's are Y's

Some Y's are Z's

Most X's are W's

Initial diagram: W<----(most)---X Y Z

Answer key inferences:

W Y

Why isn't X Z an inference?

Similarly, for question 6:

6)

Some N's are O's

No O's are P's

No P's are Q's

All Q's are R's

Initial diagram: N O P Q R

The answer key lists the following additive inferences:

N notP

R notP

Why isn't N notQ an additive inference? Could we not recycle N notP, ride the some-train, and end up with my answer?

My initial thought is perhaps I'm making a mistake when working from the middle of the problems instead of the edges? Perhaps I am also making an error regarding negatives?

Thanks in advance for your help!

I was working on the formal logic additive inference drills found on page 334 of the 2013 edition of the Logical Reasoning Bible. While doing the questions I ended up "discovering" some inferences that were not in the answer key and I would like some clarification.

1)

Some A's are B's

No B's are C's

All C's are D's

Initial diagram: A B C D

The answer keys lists the inferences as:

A notC

D notB

My question is: Why isn't A D a valid additive inference as well? Can we not recycle A notC D and ride the some-train to my answer?

Also, for question 2:

2)

All X's are Y's

Some Y's are Z's

Most X's are W's

Initial diagram: W<----(most)---X Y Z

Answer key inferences:

W Y

Why isn't X Z an inference?

Similarly, for question 6:

6)

Some N's are O's

No O's are P's

No P's are Q's

All Q's are R's

Initial diagram: N O P Q R

The answer key lists the following additive inferences:

N notP

R notP

Why isn't N notQ an additive inference? Could we not recycle N notP, ride the some-train, and end up with my answer?

My initial thought is perhaps I'm making a mistake when working from the middle of the problems instead of the edges? Perhaps I am also making an error regarding negatives?

Thanks in advance for your help!