Practice With Venn Diagrams & The Three Rule System
 
 





INSTRUCTIONS: (1) Put the syllogism given into standard form, using the rules of immediate inference (i.e., conversion, contraposition and obversion) when necessary. (2) Draw a Venn diagram and determine whether the argument is valid. Use the Aristotelian interpretation when called for. (3) For syllogisms not requiring use of the Aristotelian interpretation, determine which of the three rules of the three rule system (if any) are violated.
 

1. Every dime is a lime and every lime sublime, so every dime is sublime.

2. If every woodchuck chucks wood, and some woodchucks upchuck, then some who upchuck chuck wood.

3. No canned thing is a good ham, and some good hams are glazed. So no glazed things are canned.

4. Sometimes Harry doesn't mow the hedge. And every time he doesn't mow the hedge, he gets weeds. So sometimes Harry doesn't get weeds.

5. These are the best of times. And these times are times in which we have computers. So times in which we have computers are the best of times.

6. Some places are over the rainbow. And all places over the rainbow are happy places. So some places are happy places.

7. You should do whatever boils your crawfish. And when you two-step it boils your crawfish. So you should do the two-step.

8. Mamou is not Tee Mamou. And Tee Mamou is not my mama. So Mamou is not my mama.

9. Some people are as happy as fat rats in a cheese factory. And some things as happy as fat rats in a cheese factory escape fat cats. So some people don't escape fat cats.

10. Every day I have the blues. And when I have the blues, my Mojo is not working. So some days are times my Mojo isn't working.
 

ANSWERS:

NOTE: An 'X' followed by a number (e.g., X1, X2) indicates the diagramming of a particular sub implied by a universal premise (the premise being identified as premise 1 or 2).
Rule 1: The middle term must be distributed exactly once.
Rule 2: The subject and predicate terms of the argument cannot be distributed exactly once.
Rule 3: The number of negative premises must equal the number of negative conclusions.

1.
P1 All dimes are limes.
P2 All limes are sublime things.
C All dimes are sublime things.

No rules violated. Valid.

2.
P1 All woodchucks are things which chucks wood.
P2 Some woodchucks are things that upchuck.
C Some things which upchuck are things which chuck wood.

 No rules violated. Valid.

3.
P1 No canned hams are good hams.
P2 Some good hams are glazed things.
C No glazed things are canned.

Invalid.

4.
P1 Some times are non-times Harry mows the hedge.
P2 All non-times Harry mows the hedge are times Harry gets weeds.
C Some times are not times Harry gets weeds.

Invalid.

5.
P1 All times that are these are the best of times.
P2 All times that are these are times in which we have computers.
C All times in which we have computers are the best of times.

Only rule 1 violated. Invalid.

 6.
P1 Some places are places over the rainbow.
P2 All places over the rainbow are happy places.
C Some places are happy places.

No rules violated. Valid.

 7.
P1 All things that are you are things that should do whatever boils your crawfish.
P2 All things that are you doing the two-step are things that boil your crawfish.
C All things that are you are things that should do the two-step.

{Note: the translation has to be a little loose here, but we can still interpret the argument as a categorical syllogism.}

 Rule 1 is violated and rule 2 for the predicate term is violated. Invalid.

 8.
{P1 All things that are Mamou are non-Tee-Mamous. - by obversion:}
P1 No things that are Mamou are Tee Mamous.
P2 All Tee Mamous are non-mamas of mine.
C All Mamous are non-mamas of mine.

Rules 1 and 3 only are violated. Invalid.

 9.
P1 Some people are things as happy as fat rats in a cheese factory.
P2 Some things as happy as fat rats in a cheese factory are things that escape fat cats.
C Some people are not things that escape fat cats.

Rule 1, rule 2 for the predicate term and rule three are violated. Invalid.

10.
P1 All days are days I have the blues.
P2 All days I have the blues are times my Mojo is non-working.
C Some days are times my Mojo is non-working.

Valid.