Q13 of 18 Page 13

Given statements in (a) and (b).
Identify the statements given below as contra positive or converse of each other.
(a)
(i) If you live in Delhi, then you have winter clothes.
(ii) If you do not have winter clothes, then you do not live in Delhi.

(b)
 (i) If a quadrilateral is a parallelogram, then its diagonals bisect each other.
(ii) If the diagonals of a quadrilateral do not bisect each other, then the
quadrilateral is not a parallelogram.


(a) (i) Contra positive statement
(ii)Converse statement.

(b) (i) Contra positive statement
(ii) Converse statement.

More from this chapter

All 18 →
11
Write the contra positive 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

12
Write each of the following statements in the form of "if-then"

(i) You get a job implies that your credentials are good.

(ii) The Banana tree will bloom if it stays warm for a month.

(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.

(iv) To get an A+ in the class, it is necessary that you do all the exercises of the book.

14
Show that the statement p: "If x is a real number such that x3 + 4x = 0, then x is 0" is true by

(i) Direct method.

(ii) Method of contradiction.

(iii) Method of contra positive.

15
Show that the statement "For any real number a and b, a2 = b2 implies that a = b" is not true by giving a counter example.