Reference no: EM131098739
1. Analyze the logical forms of the following statements. Use A to represent "Alice has a dog," B to represent "Bob has a dog," and C to represent "Carol has a cat" to write each as a symbolic statement.
a. Either Alice or Bob has a dog.
b. Neither Alice nor Bob hasa dog, but Carol has a cat.
c. Either Alice has a dog and Carol has a cat, or Bob has a dog and Carol does not have a cat.
2. If D stands for "Doug is tall" and E stands for "Edie is short," what English sentences are represented by the following expressions?
a. (D ∧ E) ∨ ¬D
b. (D ∨¬E) ∧ ¬(D ∧ E)
c. ¬D ∧ [ (E ∧ D) ∨ ¬E ]
3. Make a truth table for the following formula.
(G ∨ ¬H) ∧¬(G ∧ L)
4. Use truth tables to determine which of the following formulas are equivalent to each other.
a. (J ∧ K) ∨ (¬J ∧¬K)
b. J ∨ K
c. J ∧¬K
d. ¬(¬J ∨ K)
e. (J ∧¬K) ∨ K
5. Use truth tables to determine which of the following formulas are tautologies, which are contradictions, and which are neither.
a. (M ∧ ¬N) ∨ (¬M ∧ N)
b. (M ∧ ¬N) ∧ (¬M ∧ N)
c. (¬M ∧ ¬N) ∨ (¬M ∨ N) ∨ (M ∧ ¬N)
6. Use the laws stated in the text to find simpler formulas equivalent to these formulas. Explain the reasoning that you used to find your solution.
a. ¬[ ¬Q ∨ (¬P ∧ Q) ]
b. ((P ∧ Q) ∧ ¬R) ∨ [P ∧ ¬(Q ∨ R)]
Explain what happens in the money market
: Illustrating your answer from part 2, with a money supply and demand diagram, explain what happens in the money market when the Fed increases the money supply as it has since 2007? Note that this creates an excess of supply of money that the economy ..
|
Identify the output level that would maximize total surplus
: A firm with market power faces the demand function q=4000-40p. The firm's total cost function is TC(q)=10q+.001q^2+1000. Demonstrate that the single price monopolist's profit maximizing choice of price and ouput also maximizes producer surpulus. Iden..
|
Implies that second-harmonic generation
: Backward second-harmonic generation. Part (c) of Fig. 2.1.1 implies that second-harmonic generation is radiated in the forward but is not appreciably radiated in the backward direction.
|
University charges only one price for credit hours
: A university's students have demand for credit hours given by q=30 - 0.04p, where p is the price per credit hour. If the university charges only one price for credit hours irrespective of the number of credit hours a student enrolls for, identify the..
|
Find simpler formulas equivalent
: Use the laws stated in the text to find simpler formulas equivalent to these formulas. Explain the reasoning that you used to find your solution.
|
Find the phase change undergone by its electric vector
: Find the phase change undergone by its electric vector if the refractive index of the conductor is n2=n(1+ip)
|
When measuring capital flows into and out of country
: According to David Waring, when measuring capital flows into and out of a country those capital flows include only
|
Find the annualized implied repo rate
: Find the annualized implied repo rate on a T-bond arbitrage if the spot price is 112.25, the accrued interest is 1.35, the futures price is 114.75, the CF is 1.0125, the accrued interest at delivery is 0.95, and the holding period is three months.
|
Located in the middle of residential neighborhood
: XSU is located in the middle of a residential neighborhood. The residents of the surrounding 4 blocks notice that street parking is a problem while classes are in session. Explain under what conditions (if any) the building of additional parking lots..
|