Consider the following 4-variable Boolean function

$$ F(A, B, C, D)=\Sigma m(0,1,2,3,8,9,10,11) $$

Consider $A$ as MSB, $D$ as LSB. Which one of the following options represents the minimal sum of products form for the above function?

Note: + is OR operation, • is AND operation, ' is NOT operation

Consider the digital circuit shown below with two input lines A and B, two select lines S 0 and S 1 , and an output line Y . The blocks Q and M represent active high $2: 4$ decoder and 4-to-1 multiplexer, respectively. Out of 16 possible input combinations, the number of combinations that produce $\mathrm{Y}=1$ is $\_\_\_\_$ . (answer in integer)

Note: One input combination is an instance of [A B S1 S0].

For two different persons $x$ and $y$, the predicate $M(x, y)$ denotes that $x$ knows $y$. Consider the following statement.

There is a person who does not know anyone else, but that person is known by everyone else.

Which one of the following expressions represents the above statement?

The probability density function $f(x)$ of a random variable $X$ which takes real values is

$$ f(x)=\frac{1}{3 \sqrt{2 \pi}} \exp \left(-\frac{x^2}{18}\right), x \in(-\infty,+\infty) $$

Which one of the following statements is correct about the random variable?