Consider a relational table r with sufficient number of records, having attributes A₁, A₂,....., A_n and let 1 $$ \le $$ p $$ \le $$ n. Two queries Q1 and Q2 are given below.

$$Q1: \pi_{A_1, \dots ,A_p} \left(\sigma_{A_p=c}\left(r\right)\right)$$ where is a constant

$$Q2: \pi_{A_1, \dots ,A_p} \left(\sigma_{c_1 \leq A_p \leq c_2}\left(r\right)\right)$$ where c₁ and c₂ are constants

The database can be configured to do ordered indexing on A_p or hashing on A_p. Which of the following statements is TRUE?

The simplified $$SOP$$ (Sum of product) form of the Boolean expression
$$\left( {P + \overline Q + \overline R } \right).\left( {P + \overline Q + R} \right).\left( {P + Q + \overline R } \right)$$ is

Which one of the following circuits is NOT equivalent to a $$2$$-input $$XNOR$$ (exclusive NOR) gate

Consider the following circuit involving three Dtypes flip-flops used in a certain type of Counter configuration.

If at some instance prior to the occurrence of the clock edge, $$P, Q$$ and $$R$$ have a value $$0,1$$ and $$0$$ respectively, what shall be the value of $$PQR$$ after the clock edge?