Question

1: Which of the following is not the negation of the statement "All politicians are honest"? (a) It is not true that all politicians are honest.
(b) All politicians are not honest.
(c) Not all politicians are honest.
(d) There exists a politician which is not honest.
Answer is b but can anyone explain how ??​

Answer 1

Answer:

not all politician ar honet

Answer 2

Given: The statement "All politicians are honest"

To find: The negation of the statement "All politicians are honest"

Solution:

To find out the negation of the statement we need to understand what is negation.

Negation of a statement means a negative sentence or statement that is to disapprove a statement or denying a statement.

• For the statement in option(a) It is not true that all politicians are honest. This is correct for the negation but it makes the sentence imperative, therefore, it is not the best statement for negation.

• The statement in option(b) All politicians are not honest. This statement is the perfect negation of the given statement and is to the point of the given statement.
• The statement in option(c) Not all politicians are honest. This statement is also the negation of the given statement but the order of the statement is changed therefore it cannot be said as the best negation statement.
• The statement in option(d)There exists a politician which is not honest. cannot be the negation since the meaning is completely changed. The given statement talks about all the politicians as a whole while in the option it talks about only one politician.

Final answer:

The negation of the statement "All politicians are honest" is option(b) All politicians are not honest