Question

Write the converse and contrapositive of each of the following statements:

(i) If n is an even number, then $n^2$ is even.

(ii) If two integers a and b are such that $a>b,$ then $(a-b)$ is always a positive integer.

(iii) If a $\Delta ABC$ is right angled at B, then $A{B}^2+B{C}^2=A{C}^2.$

(iv) If $\Delta ABC$ and $\Delta DEF$ are congruent, then they are equiangular.

(v) You cannot comprehend geometry if you do not know how to reason deductively.

(vi) Something is cold implies that it has low temperature.

Answer 1

(i) Its converse is :

If a number $n^2$ is even, then n is even.

Its contrapositive is:

If a number $n^2$ is not even, then n is not even.

(ii) Its converse is:

If a and b are two integers such that $(a-b)$ is a positive integer, then $a>b.$

Its contrapositive is:

If two integers a and b are such that $(a-b)$ is not a positive integer, then a is not greater than b.

(iii) Its converse is:

In a $\Delta ABC,$ if $A{B}^2+B{C}^2=A{C}^2,$ then it is right angled at B.

Its contrapositive is:

In a $\Delta ABC,$ if $(A{B}^2+B{C}^2)$ is not equal to $A{C}^2$, then it is not right angled at B.

(iv) Its converse is:

If $\Delta ABC$ and $\Delta DEF$ are equiangular, then they are congruent.

Its contrapositive is:

If $\Delta ABC$ and $DEF$ are not equiangular, then they are not congruent.

(v) Its converse is:

If you do not know how to reason deductively, then you cannot comprehend geometry.

Its contrapositive is:

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

(vi) Given statement is:

Something is cold $\Rightarrow$ it has low temperature.

Its converse is:

If something has low temperature, then it is cold.

Its contrapositive is

If something does not have a low temperature, then it is not cold.