Change the positive logic algorithm and flowchart from previous problem to reflect the following:

R=100 for S=1000-4000

R=250 for S=4001-8000

otherwise R=75

Write the VHDL code for an S-R flip-flop with a rising-edge clock. Use standard logic, and output 'X' if S = R = '1' at a rising clock edge.

The equilibrium price of coffee mugs rose sharply last month, but the equilibrium quantity was the same as ever. Three people tried to explain the situation. Which explanations could be right? Explain your logic.

In deterministic logic, the statement “$A$ implies $B$” is equivalent to its contrapositive, “not $B$ implies not $A$”. In this problem we will consider analogous statements in probability, the logic of uncertainty. Let $A$ and $B$ be events with probabilities not equal to 0 or 1. (a) Show that if $P(B|A) = 1$, then $P(A^c|B^c) = 1$. Hint: Apply Bayes’ rule and LOTP. (b) Show however that the result in (a) does not hold in general if $=$ is replaced by $\approx$. In particular, find an example where $P(B|A)$ is very close to 1 but $P(A^c|B^c)$ is very close to 0. Hint: What happens if A and B are independent?

Suppose P is a formula in propositional logic containing n variables. Approximate the worst-case complexity of an algorithm that runs through all possible true/false values of the n variables to see if there is an assignment that makes P true.

Find a logic statement involving p and q that generates each of the following truth tables .

$$\left[\begin{array}{lll} p & q & ?\\ \hline T & T & T\\ T & F & F\\ F & T & T\\ F & F & T \end{array}\right]$$

Provide a CMOS logic gate circuit that realizes the function $Y=\overline{A} B C+A \overline{B} C+A B \overline{C}.$ How many transistors are required? Explore the possibility of reducing the number of the transistors required.

Write VHDL code to implement the following logic functions using a 16 words $\times$ 3 bits ROM. W= A′B′C + C′D + ACD′. X = A′C′ + B′D. Y = BD′ + B′C′D

Use the logic game to determine whether the proposition

$$\forall x\forall y\exists z((z\gt x)\wedge (z\lt y))$$

is true or false. The domain of disclosure is $\textbf{Z}\times \textbf{Z}\times \textbf{Z}$.

Complete the input-output table for the logic network at the right.

$$\begin{array}{ccccc}p & q & p \text { OR } q & \text { NOT } q & \text { (NOT q) AND }(p \text { OR } q) \\ 1 & 1 & ? & ? & ? \\ 1 & 0 & ? & ? & ? \\ 0 & 1 & ? & ? & ? \\ 0 & 0 & ? & ? & ?\end{array}$$

Use the data in previous exercise to analyze the accounts receivable turnover ratios of H.J. Heinz Company and The Limited Brands Inc. c. Explain the logic underlying your answer in (b).

Using JK flip-flops, (a) Design a counter with the following repeated binary sequence: 0, 1, 2, 3, 4, 5, 6. (b) Draw the logic diagram of the counter.

Use the chart to link Roosevelt's reasoning to his central idea. First, identify the central idea of the speech. Then, give three examples of appeals to logic in the speech, and note how each example shapes or refines the central idea. Central Idea: ______

$$\begin{array}{|c|c|} \hline \text{EXAMPLE OF APPEAL TO LOGIC} & \text{HOW IT SHAPES OR REFINES THE CENTRAL IDEA}\\ \hline \text{ } & \text{ }\\ \hline \text{ } & \text{ }\\ \hline \text{ } & \text{ }\\ \hline \end{array}$$

Generalized De Morgan's laws for logic: $\neg (\forall xP(x))$ and $\exists x\neg P(x)$ have the same truth values. $\neg (\exists xP(x))$ and $\forall x\neg P(x)$ have the same truth values.