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. $2+3 \ne 5\; and \; 8 \nless 10$
D. $None\; of\; the \;above$

Answer 1

Hint: Negation is a complementary logical function that gives the opposite function such that it transforms the proposition “p” to another proposition “not p”. It is generally denoted as $\left( {\bar p,} \right)\left( { \sim p} \right),\left( {\neg p} \right)$. In other words, we can say that it transforms from TRUE to FALSE or from FALSE to TRUE; there is no intermediate function in between this.

In this question, we need to determine the negation of three different functions, i.e. $2 + 3 = 5$, “AND” and $8 < 10$. For this, we need to evaluate the negation of each function and then union them up.

Complete step by step answer:
 Let us consider that the function $2 + 3 = 5$ be p, and the function $8 < 10$ be q.
Now, following the general arithmetic rule:
The negation of $p:2 + 3 = 5$ is given as $\bar p:2 + 3 \ne 5 - - - - (i)$
The negation of $q:8 < 10$ is given as $\bar q:8 \nless 10- - - -(ii)$
Also, the negation of AND is OR $- - - - (iii)$
Now, following the principle of negation and equation (i), (ii) and (iii), we can say that:
The negation of $2 + 3 = 5$ and $8 < 10$ is $2+3 \ne 5 \;or\; 8 \nless 10$

Hence Option C is correct.

Note: Students should be aware while taking the negation of the functions, as we have to do the negation of the conjunction point of the function and not all the mathematical terms present in the function such as for the function $2 + 3 = 5$ we need not to transform plus (+) sign to minus (-) sign as it is not the conjunction.