Class 11 Maths Ncert Solutions Chapter 14 Ex 14.4 Mathematical Reasoning PDF

Class 11 Maths Ncert Solutions Ex 14.4

Class 11 Maths Ncert Solutions Chapter 14 Ex 14.4

 Q.1: Rewrite the statements with ‘if & then’ in 5 different ways but the sentence should convey the meaning as before.

A natural number is odd implies that its square is odd.

 

Sol:

(a).  A If the square of the natural number is said to be odd then the number is odd too.

(b).  If the square of a number is not even then the natural number which is squared is also odd.

(c).  It is mandatory that the square of a number to be not even (odd) in order to have that natural number as odd.

(d).  If the natural number is not odd then the square of that number is also not odd that is even.

(e).  In order to have the square of a number (natural number) which is odd, it is sufficient that the number (natural number) is also odd.

 

 

Q.2: Rewrite the following sentences as the converse/contrapositive of the followings:

(a).  A quadrilateral is said to be parallelogram if the diagonals bisect each other.

(b).  y is an odd number that is y is divisible by 3

(c).  If 2 lines do not intersect in the same plane, then they are said to be parallel.

(d).  If something is having a low temperature then it implies that is cold

(e).  If you are not able to deduct the reason, then you will not be able to comprehend geometry.

 

 Sol:

(a) Contrapositive   If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

Converse  If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

 

(b) Contrapositive – If y is not divisible by 3 then it is not an odd number.

Converse – If y is divisible by 3 , then it is an odd number.

 

(c) Contrapositive – If 2 lines intersect in the same plane, then they are not parallel.

Converse – If 2 lines do not intersect in the same plane, then they are parallel.

 

(d) Contrapositive – If something does not have low temperature, then it implies that it is not cold

Converse – If something is having at a low temperature, then it implies that it is cold.

 

(e) 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.

 

 

Q.3: Rewrite the following sentences with “if- then”:

(a).  You have visited Qutub Minar implies that you live in Delhi

(b).  You will pass the exam if you study hard.

(c).  In order to get A+ in the class test, you have to do all the problems of that chapter.

(d).  Parallel lines do not intersect each other in the same plane

 

Sol:

(a) If you have visited Qutub Minar then you live in Delhi.

(b) If you study hard then you will pass the exam

(c) If you want to get A+ in the class test then you have to do all the problems of the book.

(d) If two lines are parallel then they do not intersect each other in the same plane.

 

 

Q.4: Identify the contrapositive/converse from the following sentences:

(i)  If you live in Agra, then you have visited Taj Mahal

(a) If you have not visited Taj Mahal then you do not live in Agra.

(b)  If you have visited Taj Mahal then you live in Agra.

(ii) If the diagonals of the quadrilateral bisect each other then that quadrilateral is a parallelogram.

(a)   A quadrilateral is not said to be a parallelogram if the diagonals of a quadrilateral do not bisect each other.

(b)  A quadrilateral is said to be a parallelogram if the diagonals of a quadrilateral bisect each other.

 

Sol:

(i).

(a) Statement I is the contrapositive of the above mentioned statement

(b) Statement II is the converse of the above mentioned statement

 

(ii).

(a) Statement I is the contrapositive of the above mentioned statement

(b) Statement II is the converse of the above mentioned statement

 

Related Links
Ncert Exemplar Class 10 Maths Solutions Pdf Ncert Biology Book
Ncert Solutions App Ncert Exemplar Books Free Download
Ncert Exemplar Maths Ncert Exemplar Biology
Ncert Exemplar Class 8 Ncert Exemplar Class 9
Ncert Exemplar Physics Ncert Exemplar Science
Class 10 Ncert Exemplar Solutions Ncert Exemplar Class 12