Conjectures & Counterexamples
Music: Holiday Edition
Statements, Conditionals, & Biconditionals
Movies: Holiday Edition
Deductive Reasoning
100
The process of reaching a conclusion based on a pattern of examples; the assumption that an observed pattern will continue.
What is inductive reasoning?
100
Fill in the lyrics:
Jingle bells, jingle bells, ___________________. Oh what fun it is to ride __________________, hey!
Jingle bells, jingle bells, jingle all the way. Oh what fun it is to ride on a one-horse open sleigh, hey!
100
A compound statement that consists of a premise, or hypothesis, and a conclusion, which is false only when its premise is true and its conclusion is false.
What is a conditional statement?
100
In the movie Elf, what is the name given to the human child Santa accidentally carries to the North Pole?
Buddy
100
The use of general facts, rules, definitions, or properties to reach valid conclusions from given statements.
What is deductive reasoning?
200
The educated guess made using inductive reasoning based on known information and specific examples.
What is a conjecture?
200
Finish the lyrics:
"You better watch out, you better not cry, you better not ____"
pout
200
We have seen these lowercase cursive letters being used to label and identify individual statements in compound statements (such as conjunctions and disjunctions).
What are p, q, and r?
200
Who wrote the picture book that was the inspiration for the film How the Grinch Stole Christmas?
Dr. Suess
200
If p -> q is a true statement and p is true, then q is true.
**BONUS (+ 100 pts)***: Give an example.
What is the Law of Detachment?
300
An example that contradicts a conjecture and proves that it is not always true.
What is a counterexample?
300
In "Rudolph the Red-Nosed Reindeer", how many reindeer pull Santa's sleigh?
**BONUS (+100 pts)**: Name them all.
9
Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, Blitzen, and Rudolph
300
Write the converse of the conditional statement:
If it snows, then the parade will be canceled.
**BONUS (+100 pts)**: What is the truth value of the converse?
If the parade is canceled, then it has snowed.
**BONUS: False; the snow is not the only reason the parade could be canceled.
300
In what city did the 1947 film Miracle on 34th Street take place?
New York City
300
If p -> q and q -> r are true statements, then p -> r is a true statement.
**BONUS (+ 100 pts)***: Give an example.
What is the Law of Syllogism?
400
Determine the next term in the sequence.
400
This pop singer has been named the Queen of Christmas.
Mariah Carey ("All I Want for Christmas is You")
400
Identify the hypothesis and the conclusion of the conditional statement:
A number is divisible by 10 if its last digit is 0.
H: The last digit of a number is 0.
C: A number is divisible by 10.
400
In The Nightmare Before Christmas, Jack tasks a trio to "kidnap the Sandy Claws." What are the names of each individual in the trio?
**BONUS (+100 pts)**: Who are they secretly working for?
Lock, Shock, and Barrel
**BONUS**: Oogie Boogie
400
Determine whether the conclusion is based on inductive or deductive reasoning:
If you are late returning a library book, then you will be charged a $2 late fee. Ms. C returned a library book late, so she concludes that she will be charged a $2 late fee.
Ms. C is basing her conclusion on the library's policies, so she is using deductive reasoning.
500
Make a conjecture about the product of two odd numbers.
The product of two odd numbers is always an odd number.
500
How many gifts did the singer receive in "12 Days of Christmas"?
78
500
Write each biconditional as a conditional and its converse. Determine whether the biconditional is true or false.
An angle is acute if and only if it has a measure less than 90o.
Conditional: If an angle is acute, then it has a measure less than 90o.
Converse: If the measure of an angle is less than 90o, then it is acute.
The biconditional is true because both the conditional and the converse are true.
500
What renowned actor voiced the conductor for the 2004 animated film The Polar Express?
Tom Hanks
500
Determine whether the conclusion is based on inductive or deductive reasoning:
Every time Tamika has worn her favorite jersey to a football game, her school's team has won the game. Tamika is wearing her favorite jersey to the football game tonight, so she concludes that her school's team will win the game.
Tamika is basing her conclusion on a specific pattern of observations, so she is using inductive reasoning.