You are given a free running clock with a duty cycle of $$50$$% and a digital waveform $$f$$ which changes only at the negative edge of the clock. Which one of the following circuits (using clocked $$D$$ flip-flops) will delay the phase of $$f$$ by $${180^0}?$$

Consider the circuit in the diagram. The $$ \oplus $$ operator represents $$EX$$-$$OR.$$ The $$D$$ flip-flops are initialized to zeros (cleared).

The following data: $$100110000$$ is supplied to the ''data'' terminal in nine clock cycles. After that the values of $${q_2}{q_1}{q_0}$$ are

Which one of the first order predicate calculus statements given below correctly expresses the following English statement?

Tigers and lion attack if they are hungry of threatened.

Consider the following propositional statements:

$${\rm P}1:\,\,\left( {\left( {A \wedge B} \right) \to C} \right) \equiv \left( {\left( {A \to C} \right) \wedge \left( {B \to C} \right)} \right)$$
$${\rm P}2:\,\,\left( {\left( {A \vee B} \right) \to C} \right) \equiv \left( {\left( {A \to C} \right) \vee \left( {B \to C} \right)} \right)$$ Which one of the following is true?