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Implications
Chapter Name : Mathematical Reasoning
Sub Topic Code : 104_11_14_05_01
Topic Name : Implications
Sub Topic Name : Contrapositive And Converse
Introduction

• Contrapositive makes reasoning simpler. • Contrapositive and original conditional statement has always same truth. • In converse of statement hypothesis and conclusion are interchanged.

Pre-Requisites:

Knowledge of Component statements, Compound statements, Deductive reasoning, Connectives.

Real Life Question:

A builder wanted to verify that there was a right angle at the foundation. He measured lengths 39 and 52 in. on the sides of the foundation and the measure of third side is 65in. By applying converse of Pythagoras theorem can he verify a right angle at the foundation?

Key Words / FlashCards
Key Words Definitions (pref. in our own words)
Contrapositive statement A statement formed by negating both the IF-Then conditions and then interchanging the negations.
Converse statement In converse statement hypothesis and conclusion are interchanged.
Hypothesis Hypothesis is part of conditional statement just after word IF.
Learning aids / Gadgets
Gadgets How it can be used
http://www.testdesigner.com/tests/181071/logic-statements Write the contrapositive and converse of the statements.
Real life uses :

Contrapositive and converse builds logical thinking, it is a fundamental concept for indirect reasoning, contrapositive and converse statements are also helpful in writing slogans, advertisements.

Places to visit :

If you water plants then they will grow. Write contrapositive and converse of the statement.

Practical examples around us
Examples Explainations
Vaccination of children If you want to check whether each and every child in your locality has been vaccinated if we get at least one non-vaccinated child then we can disprove that every child is not vaccinated. Here we can use contrapositive of statement.
What you learn in Theory:

• Contrapositive and original conditional statement are logically equivalent. • Converse and inverse of original conditional statement are logically equivalent.

What you learn in Practice:

Contrapositive makes logical reasoning simpler.

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