HSC Arts 12th Board ExamMaharashtra State Board
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# Write the Converse, Inverse and Contrapositive of the Following Statement - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptMathematical Logic Sentences and Statement in Logic

#### Question

Write the converse, inverse and contrapositive of the following statement.
“If it rains then the match will be cancelled.”

#### Solution

Let

p : It rains,

q : the match will be cancelled.

The symbolic form of the given statement is p → q.
Converse: q → p
i.e., If the match is cancelled then it rains.
Inverse: ~p → ~q
i.e., If it does not rain then the match will not be cancelled.
Contrapositive: ~q → ~p
i.e. If the match is not cancelled then it does not rain.

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#### APPEARS IN

2016-2017 (July) (with solutions)
Question 2.1.2 | 3.00 marks
Solution Write the Converse, Inverse and Contrapositive of the Following Statement Concept: Mathematical Logic - Sentences and Statement in Logic.
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