Chapter Name : Mathematical Reasoning |
Sub Topic Code : 104_11_14_05_01 |
Topic Name : Implications |
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Sub Topic Name : Contrapositive And Converse |
• Contrapositive makes reasoning simpler. • Contrapositive and original conditional statement has always same truth. • In converse of statement hypothesis and conclusion are interchanged.
Knowledge of Component statements, Compound statements, Deductive reasoning, Connectives.
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 | Definitions (pref. in our own words) |
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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. |
Gadgets | How it can be used |
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http://www.testdesigner.com/tests/181071/logic-statements | Write the contrapositive and converse of the statements. |
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.
If you water plants then they will grow. Write contrapositive and converse of the statement.
Examples | Explainations |
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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. |
• Contrapositive and original conditional statement are logically equivalent. • Converse and inverse of original conditional statement are logically equivalent.
Contrapositive makes logical reasoning simpler.
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