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Write the contrapositive and converse of the following statements :
(i) If $x$ is a prime number, then $x$ is odd.
(ii) If the two lines are parallel, then they do not intersect in the same plane.
(iii) Something is cold implies that it has low temperature.
(iv) You cannot comprehend geometry if you do not know how to reason deductively.
(v) $x$ is an even number implies that $x$ is divisible by 4 .
(i) If $x$ is a prime number, then $x$ is odd.
(ii) If the two lines are parallel, then they do not intersect in the same plane.
(iii) Something is cold implies that it has low temperature.
(iv) You cannot comprehend geometry if you do not know how to reason deductively.
(v) $x$ is an even number implies that $x$ is divisible by 4 .
Solution:
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Verified Answer
(i) Given statement: If $x$ is a prime number, then $x$ is odd.
The contrapositive statement : If a number $x$ is not odd, then $x$ is not a prime number.
The converse statement: If a number $x$ is odd, then it is a prime number.
(ii) Given statement : If the two lines are parallel, then they do not intersect in the same plane.
The contrapositive statement : If two lines intersect in the same plane, then they are not parallel.
The converse statement : If two lines do not intersect in the same plane, then they are parallel.
(iii) Given statement : Something is cold implies that it has low temperature.
The contrapositive statement : If something is not at low temperature, then it is not cold.
The converse statement : If something is at low temperature, then it is cold.
(iv) Given statement: You cannot comprehend geometry if you do not know how to reason deductively.
The contrapositive statement: If you know how to reason deductively, then you cannot comprehend geometry.
The converse statement : If you do not know how to reason deductively, then you cannot comprehend geometry.
(v) Given statement : $x$ is an even number implies that $x$ is divisible by 4 .
It can be written as : "If $x$ is an even number, then $x$ is divisible by 4 ".
The contrapositive statement : If $x$ is not divisible by 4 , then $x$ is not an even number.
The converse statement : If $x$ is divisble by 4 , then $x$ is an even number.
The contrapositive statement : If a number $x$ is not odd, then $x$ is not a prime number.
The converse statement: If a number $x$ is odd, then it is a prime number.
(ii) Given statement : If the two lines are parallel, then they do not intersect in the same plane.
The contrapositive statement : If two lines intersect in the same plane, then they are not parallel.
The converse statement : If two lines do not intersect in the same plane, then they are parallel.
(iii) Given statement : Something is cold implies that it has low temperature.
The contrapositive statement : If something is not at low temperature, then it is not cold.
The converse statement : If something is at low temperature, then it is cold.
(iv) Given statement: You cannot comprehend geometry if you do not know how to reason deductively.
The contrapositive statement: If you know how to reason deductively, then you cannot comprehend geometry.
The converse statement : If you do not know how to reason deductively, then you cannot comprehend geometry.
(v) Given statement : $x$ is an even number implies that $x$ is divisible by 4 .
It can be written as : "If $x$ is an even number, then $x$ is divisible by 4 ".
The contrapositive statement : If $x$ is not divisible by 4 , then $x$ is not an even number.
The converse statement : If $x$ is divisble by 4 , then $x$ is an even number.
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