Counterexamples
What is a counterexample?
A counterexample is an example that disproves a statement. For example, a penguin is a bird that cannot fly.
What is the converse of "If it rains, then the ground is wet"?
The converse of "If it rains, then the ground is wet" is "If the ground is wet, then rains."
What is the inverse of "If it rains, then the ground is wet"?
The inverse of "If it rains, then the ground is wet" is "If it does not rain, then the ground is not wet."
What is the contrapositive of "If it rains, then the ground is wet"?
The contrapositive is "If the ground is not wet, then it does not rain."
What is a biconditional statement for "If it rains, then the ground is wet"?
A biconditional statement is "It rains if and only if the ground is wet."
Find a counterexample for the statement: "If a number is even, then it is divisible by 4."
A counterexample could be the number 2, which is even but not divisible by 4.
Construct a converse for the statement: "If a figure is a circle, then it is round."
The converse of "If a figure is a circle, then it is round." is "If a figure is round, then it is a circle."
Construct a Inverse for the statement: "If a figure is a circle, then it is round."
The inverse of "If a figure is a circle, then it is round." is "If a figure is not a circle, then it is not round."
Construct a contrapositive for the statement: "If a figure is a circle, then it is round."
The contrapositive is: "If a figure is not round, then it is not a circle."
Construct the biconditional form of "If a figure is circle, then it is round."
The biconditional form is "A figure is a circle if and only if it is round."
"Every prime number is an odd number."
2 is an even number (not odd) that is prime.
What is the converse of "If you study, then you will pass"?
If you will pass, then you study.
What is the inverse of "If you study, then you will pass"?
If you do not study, then you will not pass.
What is the contrapositive of "If you study, then you will pass"?
The contrapositive is: "If you do not pass, then you did not study."
What is the biconditional form of "If you study, then you will pass"?
You study if and only if you will pass.
"All shapes with equal side lengths are squares"
Construct the converse of "If Rebecca is going to shop class, then she is bringing a staple gun."
The converse of a conditional statement is "If Rebecca is bringing a staple gun, then she is going to shop class."
Construct the inverse of "If Rebecca is going to shop class, then she is bringing a staple gun.
"If Rebecca is not going to shop class, then she is not brining a staple gun."
Construct the contrapositive of "If Rebecca is going to shop class, then she is bringing a staple gun.
"If Rebecca is not bringing a staple gun, then she is not going to shop class."
Construct the biconditional form of "If Rebecca is going to shop class, then she is bringing a staple gun.
Rebecca is going to shop class if and only if she is bringing a staple gun.
"If a number is divisible by 4, it is also divisible by 8."
The number 4 is a counterexample since it is divisible by 4 but not by 8.
Construct the converse of "If a shape is a square, then it has four sides"
The converse is "If a shape has four sides, then it is a square."
Construct the inverse of "If a shape is a square, then it has four sides"
The inverse is "If a shape is not a square, then it does not have four sides."
Construct a contrapositive for the statement: "If a shape is a square, then it has four sides" is true or false.
The contrapositive is: "If a shape does not have four sides, then it is not a square."
What is the biconditional form of "If a shape is a square, then it has four sides."
"A shape is a square if and only if it has four sides" is true.