Question

Question 2 Write the contrapositive and converse of the following statements.

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

(ii) It 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

Class X1 - Maths -Mathematical Reasoning Page 338

Answer 1

(i) contrapositive statement : if x is not odd , then x is not a prime number .
converse statement : if x is odd, then x is a prime number .

(ii) contrapositive statement : if two lines are not parallel , then they do not intersect in the same plane .
converse statement : lines do not intersect in the same plane then two lines are parallel .

(iii) contrapositive statement : if the temperature of something is not low , then it is not cold.
converse statement : if something is cold then, temperature of it is low .

(iv) contrapositive statement : you can comprehend geometry , if you know how to reason deductively .
converse statement : if you don't know how to reason deductively , then you cannot comprehend geometry.

(v) contrapositive statement : if x is not divisible by 4 , then x is not an even number .
converse statement : if x is divisible by 4 , then x is an even number .