The Inverse, Converse and Contrapositive

The Inverse, Converse and Contrapositive of a Conditional Statement

Examine the statements and their relationship to the original conditional statement.

Given the tagline of one of the popular brands of soft drinks nationwide “If you drink Sprite, then you obey your thirst”. If this statement is written in different ways such as:

1. If you obey your thirst, then you drink Sprite.

2. If you do not drink Sprite, then you do not obey your thirst.

3. If you do not obey your thirst, then you do not drink Sprite.

Examine these statements and their relationship to the original conditional statement.

Guide Questions:

a. How does statement 1 relate to the given conditional statement?

b. What do you observe on the structure of statement 2 when compared to the original conditional statement?

c. What about in statement number 3, what are your observations on its structure?

d. Do you have any idea of what these statements are? If yes, what are those?

e. Does the thought of the original conditional statement changed when it was rewritten?

The Inverse, Converse and Contrapositive of a Conditional Statement

Illustrative Example 1:

• Conditional (If p, then q) : If you drink Sprite, then you obey your thirst.

• Inverse (If not p, then not q) : If you do not drink Sprite, then you do not obey your thirst.

• Converse (If q, then p) : If you obey your thirst, then you drink Sprite.

• Contrapositive (If not q, then not p) : If you do not obey your thirst, then you do not drink Sprite.

Illustrative Example 2:

• Conditional (If p, then q) : If it is raining, then the field is wet.

• Inverse (If not p, then not q) : If it is not raining, then the field is not wet.

• Converse (If q, then p) : If the field is wet, then it is raining.

• Contrapositive (If not q, then not p) : If the field is not wet, then it is not raining.

Illustrative Example 3:

• Conditional (If p, then q) : If a number is even, then it is divisible by two.

• Inverse (If not p, then not q) : If a number is not even, then it is not divisible by two.

• Converse (If q, then p) : If it is divisible by two, then the number is even.

• Contrapositive (If not q, then not p) : If it is not divisible by two, then the number is not even.

ACTIVITY 1: Judge Us!

Directions: Determine the following statement if it is converse, inverse or contrapositive of the given conditional (if-then) statement.

Multiple Choice

Conditional statement: If it’s a right angle, then its measure is 90 degrees.

_________1. If the measure of the angle is 90 degrees, then it is a right angle.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If it’s a right angle, then its measure is 90 degrees.

_________2. If the measure of the angle is not 90 degrees, then it is not a right angle.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If it’s a right angle, then its measure is 90 degrees.

_________3. If the angle is not a right angle, then its measure is not 90 degrees.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If you do your homework, then you will pass in Mathematics.

_________4. If you do not pass in Mathematics, then you do not do your homework.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If you do your homework, then you will pass in Mathematics.

_________5. If you passed in Mathematics, then you did your homework.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If you do your homework, then you will pass in Mathematics.

_________6. If you do not do your homework, then you will not pass in Mathematics.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If they are Filipinos, then they are God-fearing people.

_________7. If people are not God-fearing, then they are not Filipinos.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If they are Filipinos, then they are God-fearing people.

_________8. If people are God-fearing, then they are Filipinos.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If they are Filipinos, then they are God-fearing people.

_________9. If they are not Filipinos, then they are not God-fearing people.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If they are actresses, then they are health conscious.

_________10. If they are health conscious, then they are actresses.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If they are actresses, then they are health conscious.

_________11. If they are not actresses, then they are not health conscious.

• converse

• inverse

• contrapositive

Multiple Choice

Conditional statement: If they are actresses, then they are health conscious.

_________12. If they are not health conscious, then they are not actresses.

• converse

• inverse

• contrapositive