GATE CS 2021 Set 2 Q52 — Boolean Algebra

Consider the following Boolean expression of a function $F$ : $$F(P, Q)=(\bar{P}+Q) \oplus(\bar{P} Q)$$ Which of the following expressions is/are equivalent to $F$ ?

Which one of the following options is not a property of Boolean Algebra? Note: ${+}$ is OR operation, $\cdot$ is AND operation, and ${\prime}$ is NOT operation

Let $X$ be a $3$-variable Boolean function that produces output as $'1'$ when at least two of the input variables are $'1'$. Which of the following statement(s) is/are CORRECT, where $a, b, c, d, e$ are Boolean variables?

Which of the following Boolean algebraic equation(s) is/are CORRECT?

​​​​For a Boolean variable $x$, which of the following statements is/are FALSE?

Consider the following Boolean expression. $F=(X+Y+Z)(\overline X +Y)(\overline Y +Z)$ Which of the following Boolean expressions is/are equivalent to $\overline F$ (complement of $F$)?