Download Mathematical Statements

Name: _________________________________
Date: __________________ Set Theory and Logic ASSIGNMENT
Mathematical Statements
Write the converse, inverse, contrapositive, and identify if it is biconditional for each statement.
1. If a square’s side is 5 cm, then its area is 25 cm2.
Converse: _______________________________________________________________
Inverse: _________________________________________________________________
Contrapositive: ___________________________________________________________
Biconditional: ____________________________________________________________
2. If Kaitlyn receives a scholarship, then she will go to college.
Converse: _______________________________________________________________
Inverse: _________________________________________________________________
Contrapositive: ___________________________________________________________
Biconditional: ____________________________________________________________
3. If two distinct lines intersect, then their intersection is exactly one point.
Converse: _______________________________________________________________
Inverse: _________________________________________________________________
Contrapositive: ___________________________________________________________
Biconditional: ____________________________________________________________
4. If a number has a square root, then it is a positive number.
Converse: _______________________________________________________________
Inverse: _________________________________________________________________
Contrapositive: ___________________________________________________________
Biconditional: ___________________________________________________________
MAA 40S
Mrs. Graham
5. If x is a positive number, it is greater than or equal to zero.
Converse: _______________________________________________________________
Inverse: _________________________________________________________________
Contrapositive: ___________________________________________________________
Biconditional: ____________________________________________________________
6. If two angles have the same measure, then they are congruent.
Converse: _______________________________________________________________
Inverse: _________________________________________________________________
Contrapositive: ___________________________________________________________
Biconditional: ____________________________________________________________
7. If a polygon has ten sides, then it is a decagon.
Converse: _______________________________________________________________
Inverse: _________________________________________________________________
Contrapositive: ___________________________________________________________
Biconditional: ____________________________________________________________
8. If a triangle has a right angle, then sine law is true.
Converse: _______________________________________________________________
Inverse: _________________________________________________________________
Contrapositive: ___________________________________________________________
Biconditional: ____________________________________________________________
Key
1. If a square’s side is 5 cm, then its area is 25 cm2.
Converse: If a square’s area is 25 cm2, then its side is 5 cm.
Inverse: If a square’s side is not 5 cm, then its area is not 25 cm2.
Contrapositive: If a square’s area is not 25 cm2, then its side is not 5 cm.
Biconditional: Yes
2. If Kaitlyn receives a scholarship, then she will go to college.
Converse: If Kaitlyn will go to college, then she will receive a scholarship.
Inverse: If Kaitlyn does not receive a scholarship, then she will not go to college.
Contrapositive: If Kaitlyn will not go to college, then she will not receive a scholarship.
Biconditional: No
3. If two distinct lines intersect, then their intersection is exactly one point.
Converse: If two distinct lines intersect at exactly one point, then the lines intersect.
Inverse: If two distinct lines do not intersect, then their intersection is not one point.
Contrapositive: If two distinct lines do not intersect at exactly one point, then the lines do not
intersect.
Biconditional: Yes
4. If a number has a square root, then it is a positive number.
Converse: If a number is positive, then it has a square root.
Inverse: If a number does not have a square root, then it is not a positive number.
Contrapositive: If a number is not positive, then it does not have a square root.
Biconditional: Yes
5. If x is a positive number, it is greater than or equal to zero.
Converse: If x is greater than or equal to zero, then it is a positive number.
Inverse: If x is not a positive number, it is not greater than or equal to zero.
Contrapositive: If x is not greater than or equal to zero, then it is not a positive number.
Biconditional: No
6. If two angles have the same measure, then they are congruent.
Converse: If two angles are congruent, then they have the same measure.
Inverse: If two angles do not have the same measure, then they are not congruent.
Contrapositive: If two angles are not congruent, then they do not have the same measure.
Biconditional: Yes
7. If a polygon has ten sides, then it is a decagon.
Converse: If a polygon is a decagon, it has ten sides.
Inverse: If a polygon does not have ten sides, then it is not a decagon.
Contrapositive: If a polygon is not a decagon, it does not have ten sides.
Biconditional: Yes
8. If a triangle has a right angle, then sine law is true.
Converse: If sine law is true, then a triangle has a right angle.
Inverse: If a triangle does not have a right angle, then sine law is not true.
Contrapositive: If sine law is not true, then a triangle does not have a right angle.
Biconditional: No.