# Class 11 NCERT Solutions – Chapter 14 Mathematical Reasoning – Exercise 14.2

**Question 1. Write the negation of the following statements:**

**(i) Chennai is the capital of Tamil Nadu.**

The negation of the statement isChennai is not the capital of Tamil Nadu.

OrIt is false that chennai is the capital of Tamil Nadu.

**(ii) √2 is not a complex number**

The negation of the statement is√2 is a complex number

OrIt is false that √2 is not a complex number

**(iii) All triangles are not equilateral triangle.**

The negation of the statement isAll triangles are equilateral triangle.

OrIt is false that all triangles are not equilateral triangle.

**(iv) The number 2 is greater than 7.**

The negation of the statement isThe number 2 is not greater than 7.

OrIt is false that the number 2 is greater than 7.

**(v) Every natural number is an integer.**

The negation of the statement isEvery natural number is not an integer.

OrIt is false that every natural number is an integer.

**Question 2. Are the following pairs of statements negations of each other:**

**(i) The number x is not a rational number.**

**The number x is not an irrational number.**

Yes,they both are the negation of each other because negation of first statement isThe number x is a rational number.

which means that x is not an irrational number so the negation can also be written as

The number x is not an irrational number

Note: There are two types of number rational number and irrational number. If a number is not rational it will be irrational and vice-versa.

**(ii) The number x is a rational number.**

**The number x is an irrational number.**

Yes,they both are the negation of each other because the negation of the first statement isThe number x is not a rational number.

which means that x is an irrational number so the negation can also be written as

The number x is an irrational number

**Question 3. Find the component statements of the following compound statements and check whether they are true or false.**

**(i) Number 3 is prime or it is odd.**

The component statements are

p: Number 3 is prime

q: Number 3 is oddHere the connecting word is

ortherefore we know that if anyone the statement is true than whole statement will be true.We know that 3 is both prime as well as odd number

p -> TRUE

q -> TRUEHence, the statement is

TRUE.

**(ii) All integers are positive or negative.**

The component statements are

p: All integers are positive

q: All integers are negativeHere the connecting word is

Ortherefore we know that the statement will only be FALSE if both statement are false.we also know that 0 is neither positive nor negative.

p -> FALSE

q -> FALSEHence, the statement is

FALSE.

**(iii) 100 is divisible by 3, 11 and 5. **

The component statements are

p: 100 is divisible by 3

q: 100 is divisible by 11

r: 100 is divisible by 5Here the connecting word is

ANDtherefore we know that the statement will be FALSE if any of the statement is false.we also know that 100 is not divisible by 3 and 11 but it is divisible by 5.

p -> FALSE

q -> FALSE

r -> TRUEHence, the statement is

FALSE.

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