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Prove that the premises P → Q, Q → R, S → ¬R and P ∧ S are inconsistent.
1.)Determine if the proposition is satisfiable or not by providing any possible combination of inputs that yields a TRUE result.
(p ∧ q) ∨ (¬p ∧¬q)→r
2.)Prove or disapprove the given proposition using a truth table or rules of logic.
¬(¬p ∧ q) ∨ q ⇔ q → p
Calculate vapor pressure lowering of a solution of 2.00g of asperin(molar mass=180.15g/mol) in 50.0g of methanol (CH3OH) at 21.2°C. Pure methanol has a vapor pressure of 101 torr at this temperature.
A box of mass 20 kg is kept on a smooth horizontal surface. Another object of mass 16 kilogram is kept on the box. The two objects are connected by a light inextensible string and the string goes over a smooth pulley. If a force of 6 Newtons is applied on the box, find the acceleration of the box.
The government is considering raising the tax rate on labor income and asks you to report on the supply-side effects of such an action.
Use appropriate graphs and report directions of change, not exact magnitudes. What will happen to:
- The supply of labor
- The demand for labor and why?
- Equilibrium employment and why?
- The equilibrium before-tax wage rate and why?
- The equilibrium after-tax wage and why?
- Potential GDP?
In the economy of Nocoin, Bank deposits are $300 billion, bank reserves are $15 billion of which two-thirds are deposits with the central bank. Households and firms hold $30 billion in bank notes. There are no coins. Calculate:
- The monetary base and quantity of money.
- The banks’ desired reserve ratio and the currency drain ratio (as percentage).
Canada produces natural resources (coal, natural gas, and others), the demand for which has increased rapidly as China and other emerging economies expand.
- Explain how growth in the demand for Canada’s natural resources would affect the demand for Canadian dollars in the foreign exchange market.
- Explain how the supply of Canadian dollars would change.
- Explain how the value of the Canadian dollar would change.
- Illustrate your answer with a graphical analysis.
Suppose that yesterday the Canadian dollar was trading on the foreign exchange market at 0.75 euros per Canadian dollar and today the Canadian dollar is trading at 0.80 euros per Canadian dollar. Which of the two currencies (the Canadian dollar or the euro) has appreciated and which has depreciated today?
Colombia is the world’s biggest producer of roses. The global demand for roses increases and at the same time Colombia’s central bank increases the interest rate. In the foreign exchange market for Colombian pesos, what happens to:
- The demand for pesos?
- The supply of pesos?
- The quantity of pesos demanded?
- The quantity of pesos supplied?
- The peso-Canadian dollar exchange rate?
Banks in New Transylvania have a desired reserve ratio of 10 percent of deposits and no excess reserves. The currency drain ratio is 50 percent of deposits. Now suppose that the central bank increases the monetary base by $1,200 billion.
- How much do the banks lend in the first round of the money creation process?
- How much of the initial amount loaned flows back to the banking system as new
- deposits?
- How much of the initial amount loaned does not return to the banks but is held
- as currency?
- Why does a second round of lending occur?
- Calculate money multiplier in this example?
- What is the final increase in the quantity of money?
