Question 1: Write the negation of each of the following statements:

(i) For every x \in N, x+3 <10

(ii) There exists x \in N, x+3=10

Answer:

(i) For every x \in N, x+3 <10

Negation of the given statement: There exists a number x such that x + 3 \geq 10

(ii) There exists x \in N, x+3=10

Negation of the given statement: For every x \in N, x + 3 \neq 10

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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.