Batch 2 - Class 52 - Logic, Boolean Algebra
Preclass Exercise:
- Dudeney - 381: Can you construct a card frame, one as shown below, so that each side adds up to the same number
- Answer: following answer from Diya
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Attendance: Tishyaa, Smiti, Diya, Muskaan, Liza, Aastha, Nandini, Shubham, Hriday, Kushaan, Praharsh, Abhiram
Class Notes:
Deductive Reasoning/ Syllogism - From General truths to specific inferences
- Example: All humans are mortal. Socrates is a human. What can we infer about mortality of Socrates?
- Answer: Therefore Socrates is mortal.
- Subject of conclusion is the "Minor term", Predicate is the "Major term" and the common word is "Middle term"
- Example: No reptiles have fur. All snakes are reptiles. What can we infer about snakes and furs?
- Answer: No snakes have fur.
- Example: All rabbits have fur. Some pets are rabbit. What can we infer about pets having fur?
- Answer: Some pets have fur.
- Example: No homework is fun. Some reading is homework. What can we infer about reading being fun?
- Answer: Some reading is not fun.
- Example: All informative things are useful. Some websites are not useful. What can we say about websites being informative?
- Answer: Some websites are not informative.
Introduce Truth tables and Boolean Algebra
- Draw a truth table for one variable, like human - two values truth and false
- Draw a truth table for two variables, like human and mortal - 4 values in all
- Which rows of the truth table support the statement "All humans are mortal"
- If "Socrates is human", then what must the value of mortal be
- Introduce the notion of A implies B - draw the truth table. For "A and B", "A or B"
- What does "A implies B" say about things which are not A?
- Introduce notion of negation
- What is the value of "Not A" for all values of A?
- MathElem: Chapter 10 - Game of "Yep" and "Nope" clowns
- Yep says "All kids go to school"
- Nope says "Some kids do not go to school" (Careful about "Some kids go to school" or "All kids do not go to school"
- Yep says "All princesses wear pink"
- Nope says "Some princesses do not wear pink" (Careful about "All princesses do not wear pink")
- Match Yep statements on left with Nope statements on right
Homework:
- (Waterloo - Problem 11) There is a secret hall at Hogwart’s with magical closets. When you open a closet door, you might find Harry Potter, or you might find Voldemort. Since Hogwarts is magic, it is possible that both doors contain Harry Potter, or both doors contain Voldemort.
- (a) When you enter the secret hall, you encounter two closet doors. “One of the signs is true,” says Professor Snape,“and the other is false.”
- i. First Door: Harry is behind this door. Voldemort is behind the other.
- ii. Second Door: Harry is behind one of these doors. Voldemort is behind the other.
- Who is behind each door?
(b) You enter another secret hall and encounter two more closet doors. This time, Snape says that either both doors are true or both doors are false.
i. First Door: Harry is behind at least one of these doors.
ii. Second Door: Voldemort is behind the other door.
Who is behind each door?
References:
https://ia902701.us.archive.org/4/items/AmusementsInMathematicspdf/AmusementsInMathematics.pdf - Dudeney
Math Circles for Elementary School Students, By Natasha Rozhkovskaya (Online Google)