Question

What is converse inverse and contrapostive?

Answer 1

rhythm of the falling rain answered 6 yearGiven an if-then statement "if p, then q", we can create three related statements: 


A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause. 

For instance, “If it rains, then they will cancel school.” 
“It rains, “is the hypothesis. 
“They will cancel school,” is the conclusion. 

To form the converse of the conditional statement, interchange the hypothesis and the conclusion. 

The converse of “If it rains, then they will cancel school.” is 
“If they cancel school, then it rains.” 

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion. 

The inverse of “If it rains, then they will cancel school” is “If it does not rain, then they do not cancel school.” 

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. 

The contrapositive of “If it rains, then they will cancel school” is “If they do not cancel school, then it does not rain.” 

Summary: 
Statement If p, then q. 
Converse If q, then p. 
Inverse If not p, then not q. 
Contrapositive If not q, then not p. 

If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true. 

Example: 
Statement If a person is 18 years old, then he is a legal adult. 
Converse If a person is a legal adult, then he is 18 years old. 
Inverse If a person is not 18 years old, then he is not a legal adult. 
Contrapositive If a person is not a legal adult, then he is not 18 years old.