Consider two transactions T₁ and T₂ and four schedules S₁, S₂, S₃, S₄ of T₁ and T₂ as given below:

T₁: R₁[ x ] W₁[ x ] W₁[ y ]
T₂: R₂[ x ] R₂[ y ] W₂[ y ]
S₁: R₁[ x ] R₂[ x ] R₂[ y ] W₁[ x ] W₁[ y ] W₂[ y ]
S₂: R₁[ x ] R₂[ x ] R₂[ y ] W₁[ x ] W₂[ y ] W₁[ y ]
S₃: R₁[ x ] W₁[ x ] R₂[ x ] W₁[ y ] R₂[ y ] W₂[ y ]
S₄: R₂[ x ] R₂[ y ] R₁[ x ] W₁[ x ] W₁[ y ] W₂[ y ]

Which of the above schedules are conflict-serializable?

Let R and S be relational schemes such that R = { a, b, c } and S = { c }. Now consider the following queries on the database:

I. $$\pi_{R-S}(r) - \pi_{R-S} \left (\pi_{R-S} (r) \times s - \pi_{R-S,S}(r)\right )$$

II. $$\left\{t \mid t \in \pi_{R-S} (r) \wedge \forall u \in s \left(\exists v \in r \left(u = v[S] \wedge t = v\left[R-S\right]\right )\right )\right\}$$

III.$$\left\{t \mid t \in \pi_{R-S} (r) \wedge \forall v \in r \left(\exists u \in s \left(u = v[S] \wedge t = v\left[R-S\right]\right )\right ) \right\}$$

IV. Select R.a, R.b
    From R, S
    Where R.c = S.c

Which of the above queries are equivalent?

Consider the following three schedules of transactions T₁, T₂ and T₃.
[ Notation: In the following NYO represents the action Y (R for read, W for write) performed by transac­tion N on object O. ]

(S1) 2RA 2WA 3RC 2WB 3WA 3WC 1RA 1RB 1WA 1WB

(S2) 3RC 2RA 2WA 2WB 3WA 1RA 1RB 1WA 1WB 3WC

(S3) 2RZ 3RC 3WA 2WA 2WB 3WC 1RA 1RB 1WA 1WB

Which of the following statements is TRUE?

Consider the following schedules involving two transactions. Which one of the following statements is TRUE?

S₁: r₁(X); r₁(Y); r₂(Y); r₂(X); w₂(Y); w₁(X);

S₂: r₁(X); r₂(X); r₂(Y); w₂(Y); r₁(Y); w₁(X);