Question

Negation of the statement “Every natural number is an integer”.
A. All-natural numbers are whole numbers.
B. Every natural number is not an integer.
C. Every natural number is not a real number.
D. None of the above.

Answer 1

Hint:- We had to only place not such that the resultant statement has the opposite meaning of the given statement. Like the negation of the statement “Every triangle has three sides” can be “Not every triangle has three sides”.

Complete step-by-step solution -
As we know that the negation of any statement is the opposite of the given statement in terms of meaning.
So, to find the negation of the statement we had to place not in the statement such that it makes the given statement false.
Now there can be more than one negation of the given statement because there are many ways to grammatically express any statement.
And the negation of a statement can be logically incorrect also.
So, now let us find the negation of the statement “Every natural number is an integer”
Its negation can be,
“Every natural number is not an integer.”
Or
“It is false that every natural number is an integer.”
Or
“It is false to say that every natural number is an integer.”
Or
“It is not the case that every natural number is an integer.”

Hint:- Whenever we come up with this type of problem where we are asked to find the negation of the given statement then the trick behind the negation statement is, we had to use any of the keywords like false, not, can’t be true, not the case etc. Such that the meaning of the given statement changes or we can say that the given statement becomes false. And we should remember that there can be more than one negation possible for any statement but the meaning of all the negations will be the same because one statement can be written in many ways in grammar.