RBSE Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4

Rajasthan Board RBSE Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.4 Textbook Exercise Questions and Answers.

RBSE Class 11 Maths Solutions Chapter 14 Mathematical Reasoning Ex 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,
Answer:
Given statement:
If a natural number is odd,
then its square number is also odd.
The component statements are given by :
p : A natural number is odd.
q : The square of odd number is also odd.

Now five sentences of same meaning, in which ‘if-then’ are used:
(i) A natural number is odd it means square of natural number is odd.
(ii) A natural number is odd if and only if its square is odd.
(iii) Any natural number is odd only when its square is odd.
(iv) Any natural number is odd if and only if its square is odd.
(v) If any natural number is not odd then its square is also not odd.

Question 2.
Write the contrapositive 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) Yoa cannot comprehend geometry if you do not know how to reason deductively.
(v) x is an even number implies that* is divisible by 4. 
Answer:
(i) Given statement: If x is a prime number then x is odd.
Contrapositive : If a number x is not odd then x is not a prime number.
Converse : If a number x is odd then x is a number. 

(ii) Given statement: If two lines are parallel then they do not intersect in the same plane.
Contrapositive : If two lines intersect each other in the same plane then they are not parallel lines.
Converse : If two lines do not cut each other in the same plane then these lines are parallel.

(iii) Given statement: Something is cold implies that it has low temperature.
Contrapositive : ‘The temperature of any object is not low’ means that object is not cold.
Converse : ‘Any object has low temperature’ implies that object is cold.

(iv) Given statement: You cannot comprehend geometry if you do not know how to reason deductively.
Contrapositive : If you have knowledge that how to reason deductively then you can comprehand geometry.
Converse: If you do not have knowledge that how to reason dedcuctively then you cannot compreeand geometry.

(v) Given statement: x is an even number implies that x is divisible by 4.
Contrapositive : If x is not divisible by number 4 then x is not an even number.
Converse : If x is divisible by number 4 then x is an even number.

Question 3.
Write each of the following statements 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 an A + in class, it is necessary that you do all the exercise of the book.
Answer:
(i) Given statement: You get a job implies that your credentials are good.
Statement in the form ‘if-then’: If you have got a job then your credintials are good.

(ii) Given statement: The Bannana tree will bloom if it stays warm for a month.
Statement in the form ‘if-then’: If Bannana tree stays warm for a month then it will bloom.

(iii) Given statement: A quadrilateral is a parallelogram if its diagonals bisect each other.
Statement in the form ‘if-then’: If diagonals of a quadrilateral biset each other then quadrilateral is parallelogram.

(iv) Given statement: To get an A+ in class, it is necessary that you do all the exercises of the book.
Statement in the form ‘If-then’: If you have got A+ in class then you do all the 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 paralllogram.
Answer:
(a) Given statement : 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. (Contrapositive)
(ii) If you have winter clothes, then you live in Delhi. (Converse)

(b) Given Statement: 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 parallogram (Contrapositive.)
(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. (Converse)