1. For each of the following propositions construct a truth table and indicate whether it is a tautology (i.e., it’s always true), a contradiction (it’s never true), or a contingency (its truth depends on the truth of the variables). Also specify whether it is a logical equivalence or not. Note: There should be a column for every operator. There should be three columns to show work for a biconditional.

a) (P Λ ¬Q) ⇔ ¬(P ⇒ Q)

b) (¬? V¬?) ⇔ ¬(P Λ Q)

c) (P V Q) Λ ( ¬(? Λ Q) Λ (¬?))

d) (P ⇒ (Q Λ R)) ⇔ ((P ⇒ Q) Λ (Q ⇒ R))

e) (P ⇒ (Q ⇒ R)) ⇔ ((P ⇒ Q) ⇒ R) f) ((P V R) ⇒ (Q V S)) ⇒ ((P⇒ Q) Λ (R ⨁ S))

with biconditional and There should be a column for every operator

A DAG is a directed graph that contains no directed cycles.

Define G = (V, E) in which V is the set of all nodes as {v₁, v₂, ..., v_i , ...v_n} and E is the set of edges E = {e_i,j = (v_i , v_j ) | v_i , v_j ∈ V} .

A topological order of a directed graph G = (V, E) is an ordering of its nodes as {v₁, v₂, ..., v_i , ...v_n} so that for every edge (v_i , v_j ) we have i < j.

There are several lemmas can be inferred from the definition of DAG. One lemma is: if G is a DAG, then G has a node with no incoming edges. Given the above lemma, prove the following two lemmas:

If the graph G is a DAG, then G has a topological ordering.

If the graph G has a topological order, then G is a DAG.

(i) Consider a CMOS inverter supplied at V_DD= 5V with transistor parameters of K_N=K_P=50µA/V² and V_TN=-V_TP=1V. Then consider another CMOS inverter supplied at V_DD= 10V with the same transistor parameters. Draw the VTC of both inverters showing all regions of operation and the middle voltage VM. Verify your results using PSpice.

            (ii) Draw the square root of the CMOS inverter current versus the input voltage for the two CMOS inverters in given in part (i) biased at either V_DD=5 V or V_DD=10 V. Determine the peak current of the CMOS inverter at V_DD=5 V & V_DD=10 V. Verify your results using PSpice.

part(ii) required

PSpice for both parts

A photovoltaic module is used to supply constant 12 V that needed by a Tablet. Depending on insolation from the Sun, the photovoltaic module’s output voltage is changing between 18 V to 36 V (dc). Thus, a buck converter is used between the netbook and the photovoltaic module.

1) What is the duty ratio range of the dc/dc converter?

2) If the inductance of the buck converter inductor is 40 uH, what is the minimum switching frequency to limit the current ripple in the inductor to less than 1 A? 3) At constant 12 V, what is the minimum power consumption of the Tablet to keep the inductor current always continuous?

4) For the operation condition stated in 3), draw (not simulate and plot) the waveforms of i) switching status, ii)voltage cross the diode , and iii) inductor current; mark the values for each waveform

Using data found in Appendix E of your textbook calculate the nonstandard emf for each of the following reactions if the concentration of each of the ions in these reactions is 0.0008 molar and everything else is standard (use 298 K for the temperature, R = 8.314 J/mol-K, and F = 96,485 C/mol):

(a) 1 Cl₂(g) + 2 Cr²⁺(aq) --> 2 Cl^-(aq) + 2 Cr³⁺(aq)   E = _____ V

(b) 1 Fe³⁺(aq) + 1 Na(s) --> 1 Fe²⁺(aq) + 1 Na⁺(aq)   E = _____ V

(c) 2 Li⁺(aq) + 2 I^-(aq) --> 2 Li(s) + 1 I₂(s)   E = _____ V

(d) 1 Mn²⁺(aq) + 1 Pb(s) --> 1 Mn(s) + 1 Pb²⁺(aq)   E = _____ V

1. Many were concerned about the operation of the infamous BCCI, the international banking institution. If the government had desired to probe into the details, would this investigation have called for: a) A causal or correlational study? Why? b) A exploratory, descriptive, or hypothesis‐testing study or case analysis? Why? c) A field study, lab experiment, or field experiment? Why? d) A cross‐sectional or longitudinal study? Why?

A) In the laboratory, a general chemistry student measured the pH of a 0.566 M aqueous solution of triethylamine, (C₂H₅)₃N to be 12.221.  

Use the information she obtained to determine the K_b for this base.  

K_b(experiment) = ___

B) In the laboratory, a general chemistry student measured the pH of a 0.566 M aqueous solution of quinoline, C₉H₇N to be 9.262.

Use the information she obtained to determine the K_b for this base.  

K_b(experiment) = ___

Radiolabeled NADH was added to cell extracts containing actively respiring mitochondria. After a short

incubation period, mitochondria were isolated by subcellular fractionation using density gradient

centrifugation and analyzed for radioactivity. In one experiment, tritium labelled NADH (3H-NADH) was used.

14C-NADH was used in a second experiment. Radioactivity was associated with mitochondria in only one of

these experiments. Which one? Explain.

Some lizards have the innate ability to change color, how would this affect the experiment?

Group of answer choices

It would invalidate the entire experiment.

No effect, if measured in their native habitat.

The ability to change color or not change color would constitute excellent groups, but color changing by itself and without other data would not allow one to conclude anything.

No effect, if measured on a standard background.