consider the statements $\mathrm{P}:$ mark is rich. and $\mathrm{Q}:$ Mark if happy. Then the symbolic form of the statement "Mark is poor or he is both rich and unhappy" is _______.

Given the truth values of $\mathrm{P}$ and $\mathrm{Q}$ as $\mathrm{T}$ and those of $\mathrm{R}$ and $\mathrm{S}$ as $\mathrm{F}$, the truth value of $(\mathrm{P}\rightleftarrows \mathrm{R})\wedge (\neg \mathrm{Q}\to \mathrm{S})$ is _______.

In $\mathrm{P}\to \mathrm{Q}$ ($\mathrm{P}$ conditional $\mathrm{Q}$), the statement $\mathrm{Q}$ is called _______.

If $\mathrm{p}:$product is good. and $\mathrm{q}:$service is good. then the symbolic form of "either product is good or service is good but not both." is _______.

Which of the following is not a well-formed formula?

If the final column of the truth table for any statement formula contain truth values true and false both then statement formula is called _______.

The formulas $\mathrm{A}$ and ${\mathrm{A}}^{*}$ are said to be ________ of each other if either one can be obtained from the other by replacing $\mathrm{T}$ by $\mathrm{F}$ and $\mathrm{F}$ by $\mathrm{T}$.

${\mathrm{x}}^2+1=0$ is a statement function for universe of _______.

Let $\mathrm{C}\left(\mathrm{x}\right): \mathrm{x}$ is a cat. $\mathrm{A}\left(\mathrm{x}\right): \mathrm{x}$ is an animal. and $\mathrm{E}=${cuddle, ginger, 0, 1}, where first two elements are name of cats. Then, which of the following is true over $\mathrm{E}$?

In $\left(\mathrm{x}\right)\left(\mathrm{P}\left(\mathrm{x}\right)\wedge \left(\exists \mathrm{x}\right)\mathrm{Q}\left(\mathrm{x}\right)\right)\vee \left(\mathrm{P}\left(\mathrm{x}\right)\to \mathrm{Q}\left(\mathrm{x}\right)\right)$ the scope of the quantifier $\left(\mathrm{x}\right)$ is _______.