Question 1: Write the negation of each of the following statements:
(i) For every
(ii) There exists
Answer:
(i) For every
Negation of the given statement: There exists a number such that
(ii) There exists
Negation of the given statement: For every
Question 2: Negate each of the following statements:
(i) All the students completed their homework.
(ii) There exists a number which is equal to its square
Answer:
(i) All the students completed their homework.
Negation of the given statement: Some students did not complete their homework.
(ii) There exists a number which is equal to its square
Negation of the given statement: There exists a number which is not equal to its square.