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. (ii) The number x is a rational number. The number x is an irrational number.
The contradiction of a statement is called the negation of a statement.
(i)
The given first statement is: The number x is not a rational number. The negation of the given statement is: The number x is a rational number. The given second statement is: The number x is not an irrational number. If a number is not an irrational number, then it is obviously a rational number which is same as the negation of first sentence, thus, the given statements are negations of each other.
(ii)
The given first statement is: The number x is a rational number. The negation of the given statement is the number x is not a rational number. The given second statement is: The number x is an irrational number. If a number an irrational number then it is obvious that it is not a rational number which is same as the negation of first statement, thus the given statements are negations of each other.
The contradiction of a statement is called the negation of a statement.
(i)
The given first statement is: The number x is not a rational number. The negation of the given statement is: The number x is a rational number. The given second statement is: The number x is not an irrational number. If a number is not an irrational number, then it is obviously a rational number which is same as the negation of first sentence, thus, the given statements are negations of each other.
(ii)
The given first statement is: The number x is a rational number. The negation of the given statement is the number x is not a rational number. The given second statement is: The number x is an irrational number. If a number an irrational number then it is obvious that it is not a rational number which is same as the negation of first statement, thus the given statements are negations of each other.
