# NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning

Topics and Sub Topics in Class 11 Maths Chapter 14 Mathematical Reasoning:

Section Name |
Topic Name |

14 | Mathematical Reasoning |

14.1 | Introduction |

14.2 | Statements |

14.3 | New Statements from Old |

14.4 | Special Words/Phrases |

14.5 | Implications |

14 .6 | Validating Statements |

**NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.1**

**Question-1**

**Ans.**

**Question-2**

**Ans.**

**NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.2**

**Question-1**

**Ans.**

**Question-2**

**Ans.**

**Question-3**

**Ans.**

**NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.3**

**Question-1**

**Ans.**

**Question-2**

**Ans.**

**Question-3**

**Ans.**

**Question-4**

**Ans.**

**NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.4**

**Question-1**

**Ans.**

**Question-2**

**Ans.**

**Question-3**

**Ans.**

**Question-4**

**Ans.**

**NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.5**

**Question-1**

**Ans.**

**Question-2**

**Ans.**

**Question-3**

**Ans.**

**Question-4**

**Ans.**

**Question-5**

**Ans.**

**Class 11 Maths NCERT Solutions – Miscellaneous Questions**

**Question-1**

**Ans.**

**Question-2**

**Ans.**

**Question-3**

**Ans.**

**Question-4**

**Ans.**

**Question-5**

**Ans.**

**Question-6**

**Ans.**

**Question-7**

**Ans.**

**Q.1: State whether the following sentences are statements or not, and justify your answers.**

**(a) A month has 35 days.**

**(b) Mathematics is very tough**

**(c) Addition of two numbers such as 5 & 7 is larger than 10.**

**(d) The resultant of a square of a number is always an even number.**

**(e) The arms of a quadrilateral are having equal length.**

**(f) Answer the following questions.**

**(g) The multiplication result of two numbers such as 8 and (-1) is 8**

**(h) The interior angles summed up together results in 180 ^{0} in a triangle.**

**(i) Yesterday was a cloudy day.**

**(j) The numbers which are real are always complex numbers.**

**Q.2: Give 3 examples of each sentence which are not statements. Give justified reasons for the answers.**

**Exercise 14.2**

**Q.1: Write the opposite of the below mentioned statements:**

**(a). New Delhi is the capital of India.**

**(b). √3+1 is a complex number.**

**(c). All quadrilaterals are not squares.**

**(d). 9 is lesser than 7**

**(e). The square of every natural number is a even number**

**Q.2: State whether the following statements are opposite to each other or not.**

**(a). The number 2 is not an even number**

** The number 2 is not an odd number.**

**(b). The number 2 is an even number.**

** The number 2 is an odd number.**

**Q.3: Find out the component sentences from the below mentioned compound sentences, and determine whether they are true/ false.**

**(a). Number 5 is odd or it is a prime number.**

**(b). All integers are positive and negative.**

**(c). 1000 is divisible by 9 or 10**

**Exercise 14.3**

** ****Q.1:**

**(i). Every real number is not complex number and every rational number is a real number.**

**(ii). Square of any integer is negative or positive.**

**(iii). The sand easily heats up due to the sun but does not cool down easily at night**

**(iv). The roots for the equation x + 10 = 3x ^{2} are x = 3 and x = 2**

**Q.2: Write negation for the statements after identifying the quantifier for the statements**

**(i). There exits one number that is equal to the square of the number**

**(ii). For every number that is real ‘x’, x < x + 1**

**(iv). There exist one capital for each state of India.**

**Q.3: Check if the following statements are negation for each other. Justify your answer**

**(i). y + x = x + y is true for real numbers x and y**

**(ii). There exist real numbers x, y such that y + x = x + y**

**Q.4: State if the “Or” in the statements is inclusive or exclusive. Justify the answer**

**(i) Moon sets or sun rises**

**(ii) You must have ration card or passport for applying a driving license.**

**(iii) Integers are negative or positive**

**Exercise – 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.**

**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.**

**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**

**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.

**Exercise 14.5**

**Q.1: Prove that p: “If a is real such that a ^{3}+ 4a = 0, then a is 0″ is true **

**(i). by direct method**

**(ii). by method of contradiction**

**(iii). by method of contra positive**

**Q.2: Prove the statement “For real numbers b and a, b ^{2} = a^{2} implies that b = a” isn’t true. Give a counter example.**

**Q3: By using contrapositive method prove the following statement is true**

**p: if a is an integer and a ^{2} is even, then a is even.**