Question

Write the contrapositive and converse of the following statements
(i) If $x$ is a prime number then $x$ is odd
(ii) It 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 $4$

Answer 1

(i) The contrapositive is as follows
If a number $x$ is not odd then $x$ is not a prime number.
The converse is as follows
If a number $x$ is odd then it is a prime number.
(ii) The contrapositive is as follows
If two lines intersect in the same plane then they are not parallel.
The converse is as follows
If two lines do not intersect in the same plane then they are parallel.
(iii) The contrapositive is as follows
If something does not have low temperature then it is not cold.
The converse is as follows
If something is at low temperature then it is cold.
(iv) The contrapositive is as follows
If you know how to reason deductively then you can comprehend geometry.
The converse is as follows
If you do not know how to reason deductively then you cannot comprehend geometry.
(v) The given statement can be written as follows
If $x$ is an even number then $x$ is divisible by $4$.
The contrapositive is as follows
If $x$ is not divisible by $4$ then $x$ is not an even number.
The converse is follows
If $x$ is divisible by $4$ then $x$ is an even number.