# Class 11 NCERT Solutions- Chapter 14 Mathematical Reasoning – Exercise 14.4

**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.**

**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