Conditional Statements
This is the format of a conditional statement.
What is an if/then format?
A counterexample for the conditional statement "If the animal is a mammal, then it is a dog."
What is a cat?
*Answers may vary.
The first word that starts an indirect proof.
What is assume?
A statement in an if-then format.
The hypothesis of the conditional statement "If a number is even, then it is divisible by 2."
What is "a number is even"?
The truth value of a true statement that has been negated.
What is false?
A specific example that shows that a statement is not true in every case.
What is a counterexample?
The portion of the conditional statement that you negate.
What is the conclusion/what you are trying to prove?
The resulting statement after switching the hypothesis and conclusion of your conditional statement.
What is the converse?
A counterexample for the conditional statement "If x2=4, then x=2".
What is x=-2?
Negate the following: All even numbers are divisible by 2.
What is all even numbers are not divisible by 2?
What is a biconditional statement?
Using p to represent the hypothesis and q to represent the conclusion, give the logic notation.
What is p->q?
Using p to represent the hypothesis and q to represent the conclusion, give the logic notation of the converse.
What is q->p?
A counterexample for the conditional statement: If x2>25, then x>5.
What is x=-6?
*Answers may vary.
The first line of the indirect proof for the conditional statement. "If there are prime numbers, then there are infinitely many prime numbers".
What is "Assume that there are not infinitely many primes"?
Visual to show the relationship between the hypothesis and conclusion of a conditional statement.
What is an Euler Diagram?