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Write the converse and contrapositive of each of the following :

Question:

Write the converse and contrapositive of each of the following :

(i) If $x$ is a prime number, then $x$ is odd.

(ii) If a positive integer $\mathrm{n}$ is divisible by 9 , then the sum of its digits is divisible by $9 .$

(iii) If the two lines are parallel, then they do not intersect in the same plane.

(iv) If the diagonal of a quadrilateral bisect each other, then it is a parallelogram.

(v) If $A$ and $B$ are subsets of $X$ such that $A \subseteq B$, then $(X-B) \subseteq(X-A)$

(vi) If $f(2)=0$, then $f(x)$ is divisible by $(x-2)$.

(vii) If you were born in India, then you are a citizen of India.

(viii) If it rains, then I stay at home.

 

Solution:

(i) If x is not an odd number, then it is not a prime.

(ii) If the sum of the digits of a positive integer $n$ is not divisible by 9 , then $n$ is not divisible by 9 .

(iii) If two lines intersect in the same plane, then they are not parallel.

(iv) If the quadrilateral is not a parallelogram, then its diagonals do not bisect each other.

(v) If $A$ and $B$ are subsets of $X$ such that $(X-B)$ is not a subset of $(X-A)$, then $A$ is not a subset of B.

(vi) If $f(x)$ is not divisible by $(x-2)$, then $f(2) \neq 0$.

(vii) If you are not a citizen of India, then you were not born in India.

(viii) If I do not stay at home, then it does not rain.

 

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