Formal Logic Flaws

Question 1

Confusing Sufficiency for Necessity

Answer 1

No student is chosen for Gryffindor (/g) unless they are brave (b). Therefore, if a student exhibits bravery (b), they will be placed in Gryffindor (G).

1. G->b
   ————
2. b->G

Sentence 1 says bravery is necessary for Gryffindor. If you don’t have it you’re not getting I. Sentence 2 is basically saying any kid who is brave will be put in Gryffindor instead of any of the others.

The necessary condition doesn’t trigger the sufficient.
The necessary can occur whether or not the sufficient condition occurs.

Question 2

Denying the sufficient condition

Answer 2

The sufficient condition is mistakenly take as a requirement for the necessary condition.

Denying the sufficient condition breaks the relationship. It gives you no clue about if the necessary is in or not.

Saying
A->B
x/A
———
x/B

Is invalid. A is the sufficient (small circle) that means that something could be not a and yet be possible for it to be b or not to be b(inside or outside of the larger circle).

All birds migrate south for the winter. Monarchs aren’t birds. Therefore, monarchs don’t migrate south for the winter. —-invalid

Question 3

Affirming the Necessary

Answer 3

Yields no valid conclusions. Breaks the relationship

A->B
xB
——
xA

All Jedi use the force. Count dooku uses the force. Therefore, count dooku is a Jedi.

Affirming the necessary just means that you are looking at the bigger circle. Is the smaller circle where count dooku belongs? We simply don’t know. There isn’t enough information to support it one way or another.

Question 4

Most statements are not reversible

Answer 4

-> all arrow
-m-> most arrow are both one directional.

Most of hp’s friends are wizards. Therefore, most wizards are friends with HP.
B
B
Invalid B
A-m->B A B
——— A B
B-m->A A

Due to the possible size of the sets the wizards maybe thousands and Harry has three friends one of which is not actively a wizard. Therefore is is not possible to switch the most arrow to say that most wizards are Harry’s friends.

Question 5

All before most

Answer 5

All A are B AB
Most B are C BC
——— BC
A some C

Most people can’t play violin well. All violinists in the orchestra play violin.
Some of those violin players in the orchestra cannot play well.

This is not valid because the a set may be much smaller than the b and c sets. So most of b being c won’t matter if a is small enough that it doesn’t overlap.

Question 6

All before some