Anyone please solve fast:

Q. What is the negation of the statement 'x = y' ? Find the truth value of the following ('x=y':)

$$\begin{gathered} \left(\mathrm{i}\right) \text{'}2\ne 5 \mathrm{and} 6<4\text{'} \\ \left(\mathrm{ii}\right) \text{'}7>2 \mathrm{or} 5<3\text{'} \end{gathered}$$
 

Dear Student,

$$\begin{gathered} Let the statement \text{'}p\text{'} be: \\ p: x equals y \\ Then ~p: It is false that x equals y \\ or, ~p: x is not equal to y \\ Mathematically, \\ p: x = y \\ ~p: x \ne y \\ \left(i\right) The statement \text{'}2 \ne 5 and 6 < 4\text{'} is a compound statement with the connecting word \text{'}and\text{'}. Its component statements are: \\ q: 2 \ne 5 \\ r: 6 < 4 \\ Here, q is true and r is false. So, the compound statement \text{'}2 \ne 5 and 6 < 4\text{'} is false. \\ \left(ii\right) The statement \text{'}7 > 2 or 5 < 3\text{'} is a compound statement with the connecting word \text{'}or\text{'}. Its componenet statements are: \\ s: 7 > 2 \\ r: 5 < 3 \\ Here, s is true and r is false. So, the compound statement \text{'}7 > 2 or 5 < 3\text{'} is true. \end{gathered}$$

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