Logic in Wonderland

An Introduction to Logic through Reading Alice's Adventures in Wonderland — Student's Workbook

Nitsa Movshovitz-Hadar, Atara Shriki

• Editorial: WS EDUCATION
• Año: 2018
• ISBN:
  9789813208698
• Categoría: Education
• Categoría: Teaching Mathematics

This is a student's workbook that accompanies the teacher's guidebook of the same title. It is for students who take a course in Introduction to Logic at a teachers college, whose instructor decides to provide students with a learning environment based on reading Alice's Adventures in Wonderland, and discussing quotes from that book as a trigger for developing basic notions in Logic.

This workbook includes worksheets for independent work or for small-group activities. It is also possible to use this workbook in a workshop for in-service mathematics teachers, and also for teaching logic at high school level for capable and interested students.

Click here for Teacher's Guidebook
Contents:

• The Logical Connective AND
• The Logical Connective NOT
• The Logical Connective OR
• De Morgan's Laws
• The Empty Set
• Relations and their Properties
• The Quantifiers ALL, THERE EXISTS and ONLY
• The Logical Connective 'IF..., THEN...' (Implication)
• Necessary and Sufficient Condition

Readership: Professional college mathematics teachers, high school mathematics teachers, and high school students capable and interested in logic.
Key Features:

• A vivid treatment of a difficult subject matter
• Written by experts in the field of mathematics education
• Includes worksheets for students to work on while reading Alice in Wonderland and considering issues in mathematical logic

Chapter 1

The Logical Connective AND

Name:__________________

Worksheet 1a: Opening Exercise

Answer the questions in this worksheet in their entirety, providing as much detail as possible. If necessary, you may indicate: “I did not understand the question, therefore I have not answered it.”

1.What are the differences between the following three sentences:

A.John went to school today.

B.Did John go to school today?

C.Go to school, John!

2.Provide three mathematical statements where the differences between them are similar to the differences between the sentences in Question 1.

3.What are the differences between the following three sentences:

A.There are seven days in the week.

B.The month which follows January is August.

C.There exists a star in the universe other than EARTH where two-legged beings live.

4.Provide three mathematical statements where the differences between them are similar to the differences between the sentences in Question 3.

5.The following instruction was given in a classroom: “All those who attend the extracurricular activities: gymnastics and computers, please raise their hand.” Let us consider the following four students:

•Jane attends gymnastics and computers.

•Jonathan does not attend gymnastics and does not attend computers.

•Susan does not attend gymnastics, but does attend computers.

•Adam attends gymnastics, but does not attend computers.

Who of the four should raise their hand?

A.All four (why?)

B.Three of them (who? why?)

C.Two of them (who? why?)

D.Only one (who? why?)

E.None of them (why?)

A Look Inside the Text

Read the first two paragraphs of the book Alice’s Adventures in Wonderland, on page 1, which appears in boldface below.

Down the Rabbit-Hole

LICE was beginning to get very tired of sitting by her sister on the bank, and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, “and what is the use of a book,” thought Alice, “without pictures or conversations?”

So she was considering in her own mind (as well as she could, for the hot day made her feel very sleepy and stupid) whether the pleasure of making a daisy-chain would be worth the trouble of getting up and picking the daisies, when suddenly a White Rabbit with pink eyes ran close by her.

There was nothing so very remarkable in that; nor did Alice think it so very much out of the way to hear the Rabbit say to itself, “Oh dear! Oh dear! I shall be too late!” (when she thought it over afterwards, it occurred to her that she ought to have wondered at this, but at the time it all seemed quite natural); but when the Rabbit actually took a watch out of its waistcoat-pocket, and looked at it, and then hurried on, Alice started to her feet, for it flashed across her mind that she had never before seen a rabbit with either a waistcoat-pocket, or a watch to take out of it, and burning with curiosity, she ran across the field after it, and was just in time to see it pop down a large rabbit-hole under the hedge.

Worksheet 1b: The Logical Connective AND

1.What are the two things that happened to Alice as a consequence of it being a hot day?

2.What are the two activities that Alice must trouble herself with in order to make a daisy-chain?

3.What syntactic component helped you answer the preceding two questions?

4.Could the sentence: “When suddenly a White Rabbit with pink eyes ran close by her” be phrased instead as “when suddenly a rabbit that was white and had pink eyes ran close by her,” without changing its meaning? If not, why not? If so — do you think that there is no difference between “with” and “and”?

Worksheet 1c: The Logical Connective AND — Inference Using a Truth Table

The White Rabbit that Alice saw in Wonderland was confused and somewhat nervous. It was nervous primarily because it was afraid of the Queen of Hearts who ruled Wonderland. When the Rabbit first met Alice, it dropped the white kid gloves and the fan that it was holding. After a time, Alice heard a little pattering of footsteps in the distance and looked up eagerly to see who was coming (page 35).

Alice Meets the White Rabbit Once Again

It was the White Rabbit, trotting slowly back again, and looking anxiously about as it went, as if it had lost something; and she heard it muttering to itself, “The Duchess! The Duchess! Oh my dear paws! Oh my fur and whiskers! She’ll get me executed, as sure as ferrets are ferrets! Where can I have dropped them, I wonder?”

Alice guessed in a mo...