Consider the following circuit with initial state $${Q_0} = {Q_1} = 0.$$ The $$D$$ Flip-Flops are positive edge triggered and have set up times $$20$$ nanosecond and hold times $$0.$$

Consider the following timing diagram of $$X$$ and $$C;$$ the clock period of $$C>40$$ nanosecond which one is the correct plot of $$Y?$$

Consider two well-formed formulas in propositional logic
$$F1:P \Rightarrow \neg P$$
$$F2:\left( {P \Rightarrow \neg P} \right) \vee \left( {\neg P \Rightarrow } \right)$$

Which of the following statements is correct?

Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day ?

Let $$f:\,A\, \to B$$ be a function, and let E and F be subsets of A. Consider the following statements about images.

$$S1:\,f\,\left( {E\, \cup \,F} \right)\, = \,f\left( E \right)\, \cup \,f\,\left( F \right)$$
$$S2:\,f\,\left( {E\, \cap \,F} \right)\, = \,f\left( E \right)\, \cap \,f\,\left( F \right)$$
Which of the following is true about S1 and S2?