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.
Contrapositive - It is done by Adding 'not' to both component statements & charging order
p ⇒ q
~q ⇒ ~p
Converse - It is done by changing order of statement
p ⇒ q
then q ⇒ p
(i) Contrapositive
If a number x is not odd, then it is not prime number.
Converse
If a number x is odd, then x is a prime number.
(ii) Contrapositive
If two lines intersect in the same plane, then they are not parallel.
Converse
If two lines do not intersect in the same plane, then they are parallel.
(iii) Contrapositive
If something is not at low temperature, then it is not cold.
Converse
If something is at low temperature, then it is cold.
(iv) Contrapositive
If you know how to reason deductively, then you can comprehend geometry.
Converse
If you do not know how to reason deductively, then you can not comprehend geometry.
(v) This statement is not in if-then form
Writing in if-then form
This statement can be written as "if x is an even number, then x is divisible by 4".
Contrapositive
If x is not divisible by 4, then x is not an even number.
Converse
If x is divisible by 4, then x is an even number.