\displaystyle \textbf{Question 1: }\text{Write the negation of each of the following statements.}
\displaystyle \text{Answer:}

\displaystyle \text{(i) For every }x\in N,\ x+3<10.
\displaystyle \text{Negation: There exists }x\in N\text{ such that }x+3\geq10.

\displaystyle \text{(ii) There exists }x\in N\text{ such that }x+3=10.
\displaystyle \text{Negation: For every }x\in N,\ x+3\neq10.
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{Negate each of the following statements.}
\displaystyle \text{Answer:}

\displaystyle \text{(i) All the students completed their homework.}
\displaystyle \text{Negation: Some students did not complete their homework.}
\displaystyle \text{Or, There exists at least one student who did not complete the homework.}

\displaystyle \text{(ii) There exists a number which is equal to its square.}
\displaystyle \text{Negation: For every number, it is not equal to its square.}
\displaystyle \text{Or, For every number }x,\ x^2\neq x.
\displaystyle \\

Discover more from ICSE / ISC / CBSE Mathematics Portal for K12 Students

Subscribe to get the latest posts sent to your email.