Question

Write the negation of the following statement . 'All natural numbers are rational ' ​

Answer 1

Answer:

All rational numbers are not natural numbers.

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Answer 2

The negation of the given statement will be " All natural numbers are not rational. "

Step-by-step explanation:

The question covers the topic negation, let us first understand what negation is :

=> Negation of a statement is the opposite of the given statement.

Mathematically it can be represented as :

Negation of p will be ~p (the negation sign ' ~ ' will be in the middle of the letter)

=> Negation also changes the AND to OR and OR to AND in a statement

Mathematically it can be represented as :

Negation of (p V q) = ~(p V q)

                                = ~p ∧ ~q

=> Here the given statement is : " All natural numbers are rational. "

Negation of this statement will be

"All natural numbers are not rational "