Inverse, Converse, Contrapositive -Discrete Mathematics|UGC NET Computer Science notes

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In this post,Let us understand Inverse,Converse, and Contrapositive Statements.

Introduction:

Explanation:

In My previous post,I have already explained about the implication statement (If-then).

 Implication statement is also known as conditional statement.

It has two parts .

Hypothesis- It means condition/reason.

Conclusion-It  means result/answer.

Example:

If you study well,you will pass the exam.

Now ,Let see the first part of example is hypothesis, second part of example is conclusion.

I hope ,you understand the hypothesis and the conclusion.Inverse,Converse and Contrapositive statements  are formed from  implication statements

Now , Let us come to the concept of inverse,converse and contrapositive.

Inverse

Definition:

The inverse of a conditional statement is formed by negating both the hypothesis and the conclusion.

Example:

• Statement -If you study well,you will pass the exam
• Inverse-if  you do not study well,you will not pass the exam.
• If the statement is P → Q, the inverse is ¬P → ¬Q.

Explanation:

Inverse means negation of p and q.Look at the above example,First line is  the original statement,Second  line is the inverse statement.

Converse

Definition

The converse of a conditional statement is formed by interchanging the hypothesis and the conclusion.

Example

• Statement -If you studied well ,you pass the exam
• Converse-if you pass the exam,you studied well
• If the statement is P → Q,the converse is Q → P.

Explanation:

Converse means interchanging of p and q.Look at the above example,First line is original statement, Second  line is converse statement.

Contrapositive

The contrapositive of a conditional statement is formed by both interchanging and negating the hypothesis and the conclusion.

Example:

• Statement-If you pass the exam,you studied well.
• Contrapositive-if you did not study well,you do not pass the exam.
• If the statement is P → Q, the Contrapositive is ¬Q → ¬P.

Explanation:

Contrapositive means interchanging and negation of p and q.Look at the above example,First line is original statement, Second statement is the Contrapositive

Conclusion

I hope,this post will help you  to understand the inverse ,converse,and Contrapositive in a simple way.