Consider the relation R(P, Q, S, T, X, Y, Z, W) with the following functional dependencies.

PQ → X; P → YX; Q → Y; Y → ZW

Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.

D₁ : R = [(P, Q, S, T); (P, T, X); (Q, Y); (Y, Z, W)]

D₂ : R = [(P, Q, S); (T, X); (Q, Y); (Y, Z, W)]

Which one of the following options is correct?

Let r_i(z) and w_i(z) denote read and write operations respectively on a data item z by a transaction T_i. Consider the following two schedules.

S₁ : r₁(x) r₁(y) r₂(x) r₂(y) w₂(y) w₁(x)

S₂ : r1(x) r₂(x) r2(y) w2(y) r₁(y) w1(x)

Which one of the following options is correct?

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

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)?