Syllogism Question

[Deland Jessop]

Below is my response to assist an individual preparing for the PATI and having some difficulty with the syllogisms. Good luck everyone.

Either pigs will sit in the mud or they will lie in their stables.

The pigs will lie down.

The pigs will stay in thier stables.

The pigs will stay in the mud.

The pigs will be in the mud.

None of the above.

Either the pigs will sit in the mud or they will lie in their stables because they pigs layed down, why is the answer that they will stay in their stables? we already know that they will lie down in their stables.

Not a would equal that the pigs will not sit down. but as that wasnt a choice, I chose none of the above.

Going by the formula either a or b
b
not a
So I chose None of the above.

MY RESPONSE:

This one is testing your reasoning as well by going a bit outside the formula. The formulas are important to look at to get a basic understanding but don't over rely on them. Make sure you try and understand the reasoning behind the questions.

Option A - Correct - It states they will either sit in mud or lie in the stable and then tells you that they are laying down. Therefor they are in the stables (can't be in the mud).

Option B - Incorrect - They won't be in the mud as they are laying down.

Option C - Incorrect - Same as above just different wording.

Option D - Incorrect, as Option A logically makes sense.

Give the above some thought, and make sure you understand why the above makes sense.

Going by the formula either a or b
b
not a
The following is just restating your formula.
Either A or B.
B.
B.




Another Question

No girls have curly hair.
All curly haired people are passive.

Then most curly haired people are girls.

Then girls are passive.

Then no girls are passive.

Some passive people may be girls.



(the correct answer was given as choice d) but why?



Here the formula no a are b
all b are c
some c are not a
if some c are not a then why is d the correct answer?


MY RESPONSE:

This one is tricky, and is really testing your understanding. The easiest way to explain this is through process of elimination.

Option A - Obviously incorrect. Clearly states that no girls have curly hair.

Option B - Incorrect. Curly haired people are passive. Girls (all of whom do not have curly hair) , may or may not be passive. It doesn't state that all passive people have curly hair, it states that all people with curly hair are passive. Make sure you understand the difference between the two above statements. I'll repeat them below.

- All curly haired people are passive. (If you have curly hair you have to be passive, but you may be passive with other hair styles as well. It doesn't state that all other hair styles are not passive).

- All passive people have curly hair. (If you are passive, you have to have curly hair. You can't have straight hair and be passive with this statement. But you may have curly hair and not be passive. It doesn't state that all curly haired people are passive). Make sure you understand this reasoning.

Option C - Incorrect. For the same reasons outlined above. Some girls may still be passive, despite not having curly hair.

Option D - Correct. This is quite a vague statement, but according to the logic of the syllogism, it is correct. It states some passive people MAY be girls. (they may not be girls as well). If the statement said that some passive people ARE girls, then the statement would be wrong.

Give it some thought.

[CC9769]

I FIND THIS TO BE THE DEFINITIVE GUIDE TO SYLLOGISMS:

NO + NO : No valid conclusion
SOME + SOME: No valid conclusion
ALL + SOME:
The conclusion will start with some.
The conclusion will also contain the first object/noun after All.

A. All fungi are bacteria.
B. Some mushroom are fungi.

All bacteria are mushroom
At least some bacteria are mushroom
No mushroom are bacteria
Some mushroom are not bacteria.

The answer is: At least some bacteria are mushroom. This is because mushroom is the first object/noun after All and because some is in the first two premises.


NO + ALL :

This syllogism will have firstly have No in its answer because of the word no in one of the premises. For example:

A. No computers are televisions.
B. All cathode ray tubes are televisions.

All cathode ray tubes are computers
No cathode ray tubes are computers
All computers are cathode ray tubes
No valid conclusion

The answer is: No cathode ray tubes are computers.
Also the word cathode ray is the next object/noun after all, so if there was a reversed answer such as “ No computers are cathode rays” the answer would still remain the same.


ALL + ALL (Two types of conclusions)
1. If it has the same noun/object at the end of each premises then it will be no valid conclusion. i.e:

A. All car drivers are environmental polluters.
B. All detergents are environmental polluters.

Some detergents are environmental polluters.
All car drivers are detergents.
No car driver is a detergent.
No valid conclusion.

The answer is no valid conclusion.

2. The second type of conclusion is when the noun/object of each premises is different I.e:

A. All kitchens have cabinets.
B. All cabinets have shelves.
At least some kitchens have shelves
All shelves have kitchens
All kitchens have shelves
No valid conclusion

The answer is: All kitchens have shelves.
This is because it’s the first object/noun after All
Note: the answer will also begin with All

Another example is:

A. All paths have rocks.
B. All areas have paths.

All rocks have areas.
All areas have rocks
Not all rocks have areas.
No valid conclusion.

The first two potential conclusions are identical, however the correct answer is : All rocks have areas as area is the first object / noun after All.
You also cannot use path as it is in both premises.