Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4

Question 1.

Rewrite the following statement with â€˜if-thenâ€™ in five different ways, conveying the same meaning:

â€˜If a natural number is odd, then its square is also oddâ€™.

Solution:

- A natural number is odd implies that its square is odd.
- The natural number is odd only if its square is odd.
- If the square of a natural number is not odd, then the natural number is also not odd.
- For a natural number to be odd, it is necessary that its square is odd.
- For a square of a natural number to be odd, it is sufficient that the number is odd.

Question 2.

Write the contrapositives and converses of the following statements:

- If x is a prime number, then x is odd.
- If the two lines are parallel, then they do not intersect in the same plane.
- Something is cold implies that it has low temperature.
- You cannot comprehend geometry, if you do not know how to reason deductively.
- x is an even number implies that x is divisible by 4.

Solution:

1. Contrapositive statement:

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

Converse statement:

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

2. Contrapositive statement:

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

Converse statement:

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

3. Contrapositive statement:

If the temperature of something is not low, then it is not cold.

Converse statement:

If something has low temperature, then it is cold.

4. Contrapositive statement:

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

Converse statement:

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

5. 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.

Question 3.

Write each of the following statements in the form â€˜if thenâ€™:

- You get a job implies that your credentials are good.
- The banana trees will bloom, if stays warm for a month.
- A quadrilateral is a parallelogram, if its diagonals bisect each other.
- To get an A in the class, it is necessary that you do all exercises of the book.

Solution:

- If you get a job, then your credentials are good.
- If it stays warm for a month, then the banana tree will bloom.
- If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
- If you want to get an A in the class, then you do all exercises of the book.

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) Contrapositve statement

(ii) Converse statement

(b)

(i) Contrapositive statement

(ii) Convese statement