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Converse, Inverse, and Contrapositive - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Converse, Inverse, and Contrapositive is considered one the most difficult concept.
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35 Questions around this concept.
Solve by difficulty
The contrapositive of the statement ‘If two numbers are not equal, then their squares are not equal’, is :
The contrapositive of the statement “I go to school if it does not rain” is :
The negation of the statement “If I become a teacher, then I will open a school” is
Which of the options is a sufficient condition for $p \Leftrightarrow q$ to be true?
Consider the following statements :
P : Suman is brilliant.
Q : Suman is rich.
R : Suman is honest.
The negation of the statement,
"Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as
Consider the following three statements :
$P$ : 5 is a prime number.
Q : 7 is a factor of 192.
$R$ : L.C.M of 5 and 7 is 35 .
Then the truth value of which one of the following statement is true?
Contrapositive of the statement ''If two numbers are not equal, then their squares are not equal.'' is:
Find the correct negation of
p : America is not in India
The contrapositive of the following statement, “If the side of a square doubles, then its area increases four times”, is
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Use NowThe negation of $p \vee(\sim p \wedge q)$
Concepts Covered - 1
Converse, Inverse, and Contrapositive
Given a statement of the form: "if p then q", then we can create three related statements:
Converse
To form the converse of the conditional statement, interchange p and q.
The converse of “If you are born in some country, then you are a citizen of that country” is “If you are a citizen of some country, then you are born in that country.”
Inverse
To form the inverse of the conditional statement, take the negation of both the p and q.
The inverse of “If you are born in some country, then you are a citizen of that country” is “If you are not born in some country, then you are not a citizen of that country.”
Contrapositive
To form the contrapositive of the conditional statement, interchange the p and q and take negation of both.
The Contrapositive of “If you are born in some country, then you are a citizen of that country” is “If you are not a citizen of that country, then you are not born in some country.”
These can be summarized as
$\begin{array}{|c|c|c|}\hline \text { Statement } & \mathrm{\;\;\;}{\text { If } p, \text { then } q} \mathrm{\;\;\;}& \mathrm{\;\;\;}p\rightarrow q \mathrm{\;\;\;}\\ \hline \text { Converse } & \mathrm{\;\;\;}{\text { If } q, \text { then } p} \mathrm{\;\;\;}&\mathrm{\;\;\;}q\rightarrow p \mathrm{\;\;\;} \\ \hline \text { Inverse } & \mathrm{\;\;\;}{\text { If not } p, \text { then not } q} \mathrm{\;\;\;}& \mathrm{\;\;\;}(\sim p) \rightarrow(\sim q) \mathrm{\;\;\;} \\ \hline \text { Contrapositive } & \mathrm{\;\;\;}{\text { If not } q, \text { then not } p} \mathrm{\;\;\;}& \mathrm{\;\;\;}(\sim q) \rightarrow(\sim p) \mathrm{\;\;\;}\\ \hline\end{array}$
Note:
- A given statement and its contrapositive have the same meaning
- As inverse is the contrapositive of converse, so it has the same meaning as the converse
- A given statement (= contrapositve) is NOT the same as its converse (=Inverse)
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