# Geometry: Logic Statements

## Problems 3

Summary Problems 3

Problem : State the inverse, converse, and contrapositive of the following statement.

p: If the worker is injured, then the family sues.

Inverse: If the worker is not injured, then the family does not sue.
Converse: If the family sues, then the worker is injured.
Contrapositive: If the family does not sue, then the worker is not injured.

Problem : State the inverse, converse, and contrapositive of the following statement.

p: If the enemy retreats, the general will pursue them.

Inverse: If the enemy does not retreat, the general will not pursue them.
Converse: If the general pursues them, then the enemy will retreat.
Contrapositive: If the general does not pursue them, then the enemy will not retreat.

Problem : Given the following statement, decide its truth value, and then decide the truth values of its inverse, converse, and contrapositive.

p: If a polygon has four sides, it is a pentagon.

Statement: F
Inverse: F
Converse: F
Contrapositive: F

Problem : Given the following statement, decide its truth value, and then decide the truth values of its inverse, converse, and contrapositive.

p: If a triangle is obtuse, then it has one obtuse angle.

Statement: T
Inverse: T
Converse: T
Contrapositive: T

Problem : Given the following statement, decide its truth value, and then decide the truth values of its inverse, converse, and contrapositive.

p: If two triangles are congruent, then they are similar.

Statement: T
Inverse: F
Converse: F
Contrapositive: T