Square of Opposition

Using the Square of Opposition and the Categorical Operations, determine whether the following inferences follow ( Yes and No question, one or two-sentence explain)

1. Some mistakes are not enduring tragedies. Therefore, no mistakes are enduring tragedies.
2. All married bachelors are polygamists. Therefore, it is false that some married bachelors are not polygamists.
3. No expensive lawsuits are friendly exchanges. Therefore, no unfriendly exchanges are inexpensive lawsuits.

Diagram and state whether the following syllogisms is valid ( need a diagram, there is sample of diagram at materials )

1. Some M are not P. All M are S.
   Some S are not P.
2. A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie.

You meet five inhabitants: Zoey, Bart, Rex, Dave and Alice. Zoey tells you, Rex is a knight and Dave is a knave.' Bart claims that Rex is a knave or Zoey is a knave. Rex tells you that only a knave would say that Alice is a knave. Dave tells you,Alice is a knave.' Alice tells you, `Either I am a knight or Bart is a knight.'

Can you determine who is a knight and who is a knave? If so, who is who? For full credit, you must prove your answer.

Sample Solution