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

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

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

(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