Question

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 $4$.

Answer 1

Given statement:
$i)$ If $x$ is a prime number, then $x$ is odd.

Contrapositive sentence: If a number $x$ is not odd, then it is not a prime number.

Converse sentence: If a number $x$ is odd, then $x$ is a prime number.

$ii)$ Given statement:
If the two lines are parallel, then they do not intersect in the same plane.

Contrapositive sentence: If two lines intersect in the same plane, then they are not parallel.

Converse sentence: 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.

Contrapositive sentence: If something does not have low temperature, then it is not cold.

Converse sentence: 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.

Contrapositive sentence: If you know how to reason deductively, then you can comprehend geometry.

Converse sentence: 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 $4$.

Contrapositive sentence: If $x$ is not divisible by $4$, then $x$ is not an even number.
Converse sentence: If $x$ is divisible by $4$ then $x$ is an even number.