Conjectures and Counterexamples
An if-then statement is called a ______________.
What are the two parts of a If-Then Statement?
Hypothesis and Conclusion
How many children does Mrs. Beigel have?
What is 3
If the hypothesis and conclusion are switched, Is it converse, inverse, or contrapositive?
What is converse
Determine if the conditional statement is true or false: "If it is D period, then I am supposed to be in Geometry class"
True
_______ is a statement to prove a conditional false.
What is a Counter Example
"if I get paid, then I will work." What is the hypothesis of the previous statement?
I get paid
How many of Mrs. Beigel's children are in high school?
Original Statement: "If he is Spiderman, then his name is Peter Parker." New Statement: "If he is NOT Spiderman, then his name is NOT Peter Parker." Is this converse, inverse, or contrapositive?
Inverse
Determine the truth value of the converse of the statement: "If I score a 100% on the test, then I have the highest grade in the class."
False, converse: If I have the highest grade in the class, then I scored a 100% on the test - The highest grade may only be a 98%.
To find a counterexample, which part of the conditional statement must be true and which part must be false?
Assume the hypothesis is true and the conclusion is false.
"If I work then I will get paid." What is the conclusion of the previous statement?
I will get paid.
How many of Mrs. Beigel's children are in college?
What is 1
"If an angle is acute, then it is 50 degrees." Is this always true?
False
Determine the truth value of the inverse of the statement: "If a student is in Mrs. Beigel's classroom, then they are in math class."
False, they could have another math teacher for math class.
Provide a counterexample to the following statement. "All superheroes have super powers."
False. Batman does not have super powers.
Write the statement in if-then form. "Running will make me healthier."
"If I go running, then it will make me healthier."
What is Lacey
Provide a counterexample to the statement: "If an angle is acute, then it is 50 degrees."
Numbers between 0 and 90 but not 50 degrees are counterexamples.
Determine the truth value of the contrapositive of the statement: "If the sum of two angles is 180 degrees, then the two angles are supplementary."
True
Provide a counterexample to the following statement. "All lines will eventually intersect with each other."
False. Parallel lines will never intersect.
What is the hypothesis of the statement? "If I use the midpoint formula, then my answer is a coordinate pair."
hypothesis: I use the midpoint formula
What town does Mrs. Beigel live in?
Write the contrapositive of the statement: " If I am alive, then I breathe." Make sure it is grammatically correct.
"If I am not breathing, then I am not alive."
Determine the truth value of the contrapositive of the statement: "If I am a student at Nashoba High School, then I know that the Wolves football team Football won the game."
False- contrapositive: If I do not know that Wolves Football won the Homecoming game, then I am not a student at Nashoba High School. - You may not be aware but can still be a student at NRHS.