Question 1. Write the negation of the following statements:
(i) Chennai is the capital of Tamil Nadu.
The negation of the statement is
Chennai is not the capital of Tamil Nadu.
Or
It 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
Or
It is false that √2 is not a complex number
(iii) All triangles are not equilateral triangle.
The negation of the statement is
All triangles are equilateral triangle.
Or
It is false that all triangles are not equilateral triangle.
(iv) The number 2 is greater than 7.
The negation of the statement is
The number 2 is not greater than 7.
Or
It is false that the number 2 is greater than 7.
(v) Every natural number is an integer.
The negation of the statement is
Every natural number is not an integer.
Or
It 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 is
The 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 is
The 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 odd
Here the connecting word is or therefore 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 -> TRUE
Hence, the statement is TRUE.
(ii) All integers are positive or negative.
The component statements are
p: All integers are positive
q: All integers are negative
Here the connecting word is Or therefore 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 -> FALSE
Hence, 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 5
Here the connecting word is AND therefore 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 -> TRUE
Hence, the statement is FALSE.