In middle school, you learned that positive and negative integers have opposite signs. In science, you learned that up and down are opposite directions. With conditional statements, sometimes the opposite of a hypothesis and conclusion happens. Those statements are called the inverse of a conditional statement.

Navigators and pilots will often respond “negative” over the radio to answer a question, “no.” You have seen this in movies and television shows. Using the word “negative” in this sense indicates an opposite response. In Geometry, we call that opposite response negation.

Definition: The negation of a statement is stating the opposite meaning of the original statement. 

The negation of a true statement is false, and the negation of a false statement is true.

Examples:
Click on the blanks to check your answer.

Statement: Texas is the Lone Star State. (This is the true statement.)
Negation: Texas is Interactive button. Assistance may be required. ____ NOT   the Lone Star State.(This is the false statement)

Statement: Paris is not in Texas.
Negation: Paris Interactive button. Assistance may be required. ____ is  in Texas.

The inverse of a conditional statement is when both the hypothesis and conclusion are negated; the “If” part or p is negated and the “then” part or q is negated.

• In Geometry the conditional statement is referred to as p → q.
• The Inverse is referred to as ~p → ~q where ~ stands for NOT or negating the statement.

Examples: 

Conditional statement:	If three points lie on a line,	then the three points are collinear
	Hypothesis / p	Conclusion / q

Inverse statement:	If three points DO NOT lie on a line,	then the three points are NOT collinear
	Hypothesis / p	Conclusion / q

Fill in the blanks.

Conditional statement: If the sun is shining, then it is not raining.

• The hypothesis or p is: Interactive button. Assistance may be required. __________ The sun is shining .
  
  
• The conclusion or q is:Interactive button. Assistance may be required. __________ It is not raining .
  
  
• The Inverse statement is: Interactive button. Assistance may be required. __________ If the sun is NOT shining, then it IS raining .
  
  
• A geometrical or logical representation of the converse statement is Interactive button. Assistance may be required. __________ ~ p → ~ q .