Conjectures
Logic
Conditional Statements
Inverse, Converse or Contrapositive
Deductive Reasoning
100
Write a conjecture about the following value: The sum of two odd numbers
What is an even number?
100
Give the negation of the following statement: A rectangle is a quadrilateral.
What is a rectangle is not a quadrilateral?
100
Identify the hypothesis and conclusion of the following conditional statement: If the forecast is rain, then I will take an umbrella
What is the forecast is rain is the hypothesis, and I will take an umbrella is the conclusion?
100
Give the converse of the following true statement and determine whether the converse is true or false: If you live in Chicago, you live in Illinois.
What is If you live in Illinois, you live in Chicago? F
100
Determine whether the following conclusion is based on inductive or deductive reasoning: All of the signature items on the restaurant's menu are noted with a special symbol. Kevin orders a menu item that has this symbol next to it, so he concludes that the menu item that he has ordered is a signature item.
What is inductive reasoning? (The pattern is the symbol is only placed next to signature items on the menu)
200
Write a conjecture that describes the pattern in the following: $4.50, $6.75, $9.00
What is $2.25?
200
Use the following statements to write a compound statement for each conjunction. Then find its truth value. p: January is a fall month. q: January has only 30 days. r. January 1 is the first day of the new year. p^r
What is January is a fall month and January is the first day of the new year? Truth value: F
200
Identify the hypothesis and conclusion of the following conditional statement: Another performance will be scheduled if the first one is sold out.
What is the first one is sold out is the hypothesis, and another performance will be scheduled is the conclusion?
200
Give the inverse of the following true statement and determine whether the inverse is true or false. If two angles have the same measure, then the angles are congruent.
What is If two angles do not have the same measure, then the angles are not congruent? T
200
Using the Law of Detachment, determine whether the conclusion is valid based on the given information. Explain your reasoning. Given: If Mika goes to the beach, she will wear sunscreen. Mika is wearing sunscreen. Conclusion: Mika is at the beach.
What is invalid? Mika may be at the pool or working in her garden.
300
Write a conjecture that describes the pattern of the following sequence: 3, 3, 6, 9, 15
What is each element in the pattern is the sum of the previous two elements?
300
Use the following statements to write a compound statement for each conjunction. Then find its truth value. p: January is a winter month. q: January has 31 days. r. January 1 is the first day of the new year. q^p
What is January has 31 days and January is a winter month? Truth value: T
300
Identify the hypothesis and conclusion of the following conditional statement and give answer in if-then form Points will be deducted from any paper turned in after Wednesday's deadline.
What is If a paper is turned in after Wednesday's deadline, then points will be deducted?
300
Give the contrapositive of the following true statement and determine whether the contrapositive is true or false. All whole numbers are integers.
What is If it is not an integer, then it is not a whole number? T
300
Determine whether the conclusion is valid based on the information given. Explain your reasoning. Given: If a primate is an ape, then it does not have a tail Koko is a primate who does not have a tail. Conclusion: Koko is an ape.
What is invalid? Koko may be another type of primate that does not have a tail.
400
Make a conjecture about the following geometric relationship: the measure of each angle of an equilateral triangle.
What is congruent?
400
Use the following statements to write a compound statement for each disjunction. Then find its truth value. p: -3 - 2 = -5 q: Vertical angles are congruent. r: 2+8>10 s: The sum of the measure of complementary angles is 180 p or s
What is -3 - 2 = -5 or the sum of the measure of complementary angles is 180? Truth value: T
400
Identify the hypothesis and conclusion of the following conditional statement and give answer in if-then form: The sum of the measures of two supplementary angles is 180.
What is If two angles are supplementary, then the sum of their measures is 180?
400
Give the inverse of the following true statement and determine whether the inverse is true or false. A hamster is a rodent.
What is If it is not a hamster, it is not a rodent? F
400
Using the Law of Syllogism, determine which statement follows logically from the given statements. (1) If you like musicals, then you enjoy theater productions. (2) If you are an actor, then you enjoy theater productions. a. If you are an actor, then you like musicals. b. If you like musicals, then you are an actor. c. If you do not enjoy musicals, then you are an actor. d. There is no valid conclusion.
What is d?
500
Make a conjecture about the following geometric relationship: the relationship between the set of points in a plane equidistant from point A.
What is a circle?
500
Use the following statements to write a compound statement for each disjunction. Then find its truth value. p: -3 - 2 = -5 q: Vertical angles are congruent. r: 2+8>10 s: The sum of the measure of complementary angles is 180 ~p or ~r
What is -3 - 2 does not = -5 or 2+8 is not >10? Truth value T
500
Determine the truth value of the following conditional statement. If true, explain your reasoning. If false, give a counterexample: If the square root of x = -1, then -1 squared = 1
What is True. Any conditional statement with a false hypothesis is always true?
500
If the conditional statement is true, is the inverse true or false?
What is False?
500
Using the Law of Syllogism, determine the statement that follows logically from the given statements. Given: Ballet dancers like classical music. If you like classical music, then you enjoy opera.
What is If you are a ballet dancer, then you enjoy opera?
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