Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi. (b) If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
(a) The given statement is: If you live in Delhi, then you have winter clothes.
The contrapositive of the given statement is: If you do not have winter clothes, then you do not live in Delhi.
The converse of the given statement is: If you have winter clothes, then you live in Delhi.
(i) The statement is given as: If you do not have winter clothes, then you do not live in Delhi. This statement is same as the contrapositive of the given statement, thus statement (i) is contrapositive of the statement (a).
(ii) The statement is given as: If you have winter clothes, then you live in Delhi. This statement is same as converse of the given statement, thus statement (ii) is the converse of statement (a).
(b) The given statement is: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
The contrapositive of the given statement is: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.
The converse of the given statement is: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
(i) The statement is given as: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. This statement is same as the contrapositive of the given statement, thus statement (i) is contrapositive of the statement (b).
(ii) The statement is given as: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. This statement is same as converse of the given statement, thus statement (ii) is the converse of statement (b).
(a) The given statement is: If you live in Delhi, then you have winter clothes.
The contrapositive of the given statement is: If you do not have winter clothes, then you do not live in Delhi.
The converse of the given statement is: If you have winter clothes, then you live in Delhi.
(i) The statement is given as: If you do not have winter clothes, then you do not live in Delhi. This statement is same as the contrapositive of the given statement, thus statement (i) is contrapositive of the statement (a).
(ii) The statement is given as: If you have winter clothes, then you live in Delhi. This statement is same as converse of the given statement, thus statement (ii) is the converse of statement (a).
(b) The given statement is: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
The contrapositive of the given statement is: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.
The converse of the given statement is: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
(i) The statement is given as: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. This statement is same as the contrapositive of the given statement, thus statement (i) is contrapositive of the statement (b).
(ii) The statement is given as: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. This statement is same as converse of the given statement, thus statement (ii) is the converse of statement (b).
