Prove that the following sets of premises are consistent.

1. If salaries are raised life becomes more expensive.
   If salaries are not raised life becomes more expensive.
   It is so that life becomes more expensive.

2. Either costs do not increase or prices rise.
   Either costs increase or prices do not rise.

3. If salaries are raised the cost of living increases.
   It is not the case that if the cost of living increases salaries are raised

4. Either there is inflation or taxes rise.
   Either there is no inflation or taxes do not rise.

5. e. There is neither inflation nor depression.
   Either there is depression or not.
   Either there is no depression or there is inflation.

6. All who exert themselves thrive.
   Not all that thrive exert themselves.

7. Some TV presenters do not speak clearly.
   It is not the case that some who speak clearly are TV presenters.

8. Not everyone is present.
   Those present are not all the ones.
   

9. No actor is a director.
   Someone who does not direct is not an actor.

10. No fake is consistent.
    Who is consistent does not dread ill.
    No fake dreads ill.

From the following witnesses and suspects depositions, decide which ones are mutually inconsistent.

The smuggling came by boat; the boat was Mr. A’s, who knew his business.
If the smuggling came in that boat, Mr. C had nothing to do with the matter.
The shipment was transported to New Jersey by Mr. C.
Mr. B financed the operation.
At least one of A and B had something to do with the business.
At least one of B and C had something to do with the business.
A is innocent, but B and C are guilty.
B is innocent, and so is C, but not A.
C is innocent, but A and B are guilty.

From the previous exercise, select the less possible number of sets of premises consistent with each other.

Present a counterexample to refute each one of the following universal propositions or definitions.

No metal is gold.
All solids are electrical conductors.
No genius is infirm.
A circle is a closed curved line.
A State is an organized society.
All illnesses have a cure.
Science is systematized knowledge.
When the demand for an item increases its price always rises.
All numbers lower than seven are prime numbers.
Prime number is every number divisible by the unit.
Good consists in the search of pleasure.
Everyone who does good deeds is rewarded.