Question

Negation of $2+3=5$ and $8<10$ is

• A. $2+3\ne 5$ and $8<10$
• B. $2+3=5$ and $8\nless 10$
• C. $2+3\ne 5$ or $8\nless 10$
• D. None of these

Answer 1

The correct option is C

$2+3\ne 5$ or $8\nless 10$

Explanation for the correct answer:

Obtaining the negation form of the given equation:

The given statement is $2+3=5$ and $8<10$ which can be considered as,

$p:2+3=5$ and $q:8<10$ and it's in the form of $p\wedge q$

Now, taking its Negation we get,

$~\left(p\wedge q\right)=~p\vee ~q$

Negation of $p\text{and}q$is given as

$$\begin{gathered} ~p\Rightarrow 2+3\ne 5 \\ ~q\Rightarrow 8\nless 10 \end{gathered}$$

Substituting this in the negation equation we get

$~\left(p\wedge q\right)=2+3\ne 5\vee 8\nless 10$

Thus, the negation of the given statement can be written as $2+3\ne 5$ or $8\nless 10$

Hence, option (C) is the correct answer.