QUESTION 1:

John, who always keeps his word, said to his wife, Michelle: “On your next birthday, I will give you this gold necklace as a present but only if it is a surprise.” (He shows her a gold necklace).

Did Michelle think that John would give her the gold necklace as a present?

QUESTION 2:
This is a continuation of the previous question…

John, who always keeps his word, said to his wife, Michelle: “On your next birthday, I will give you this gold necklace as a present but only if it is a surprise.” (He shows her a gold necklace).

Do you think John gave Michelle the gold necklace as a present on her birthday?

QUESTION 3:

Three students, Abraham, Isaac and Jacob, wrote a science project. When they handed it in, the teacher found a serious error in the second part of the project. The teacher wanted to find out who made the mistake and called in the students one by one. Each of the students made a statement as follows:

Abraham: I did not make a mistake, Isaac did, and in any case, I wrote a different part of the project. Isaac: Jacob made the mistake. Even great scientists make mistakes sometimes. Jacob: I did not make a mistake. By the way, Abraham did write a different part of the project.

The teacher knew that one of the sentences that each student made is true, and the other is false. Which student made the mistake in the second part of the project?

QUESTION 4:

On Smullyan’s ‘Isle of Dreams’ the residents are always awake during the day, and always sleep at night. When they sleep, they dream dreams that seem very realistic, and are a continuation of whatever happened during the day.

When they wake up, their real lives seem to be a continuation of their dream life, so that sometimes they don’t know if they are asleep or awake!

The residents of the island are of two types:

• Diurnals – who believe that whatever happens when they are awake is true, and whatever happens when they are asleep is false.
• Nocturnals – who believe that whatever happens when they are awake is false, and whatever happens when they are asleep is true.

Once one of the residents thought that he was nocturnal. Was he right?

Question 5:

This is a continuation to the previous quesion.

Recall that the residents of the island are of two types:

• Diurnals – who believe that whatever happens when they are awake is true, and whatever happens when they are asleep is false.
• Nocturnals – who believe that whatever happens when they are awake is false, and whatever happens when they are asleep is true.

Once one of the residents thought that he was nocturnal. Was he awake or asleep at the time?