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Class 11 NCERT Solutions- Chapter 14 Mathematical Reasoning – Exercise 14.4
  • Last Updated : 28 Dec, 2020

Question 1. Rewrite the following statement with “if-then” in five different ways conveying the same meaning.

If a natural number is odd, then its square is also odd.

Solution:

(i) An odd natural number implies that its square is odd.

(ii) If a natural number is odd it means that its square is also odd.

(iii) A natural number is odd only if its square is odd.

(iv) If the square of a natural number is not odd, then the natural number is not odd.



(v) For the square of a natural number to be odd, the natural number should be odd.

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

Solution:

(i) Contrapositive:



If a number x is not odd, then x is not a prime number.

Converse:

If a number x is odd, then it is a prime number

(ii) Contrapositive:

If two lines intersect in the same plane, then the two lines are not parallel.

Converse:

If two lines do not intersect in the same plane, then they are parallel

(iii) Contrapositive:

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

Converse:

If something is at low temperature, then it is cold.

(iv) Contrapositive:

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

Converse:

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

(v) Contrapositive:

If x is not divisible by 4, then x is not an even number.

Converse:

If x is divisible by 4, then x is an even number.

Question 3. Write each of the following statement in the form “if-then”.

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

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

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

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

Solution:

(i)To get a job you should have good credentials

(ii) For the banana trees to bloom, it should stay warm for a month.

(iii) For a quadrilateral to be a parallelogram, it’s diagonals should bisect each other.

(iv) If you do not do all exercises of the book, then you would not get an A+ in the class.

Question 4. 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.

Solution:

(a) (i) Contrapositive

(ii) Converse

(b) (i) Contrapositive

(ii) Converse

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