16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement is a sentence that is true. ________(b) In logic, p q refers to the "inclusive or, " true when either p or q or both are true. ________(c) The phrase "not p and not q" means "not both p and q." ________(d) The conditional statement p q is true if p is false. ________(e) The negation of p q is p ~q. #5....
#7. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) k in Z k2 + 9 = 0. ________(b) m, n in N, 5m 2n is in N. ________(c) x in R, if |x − 2| < 3, then |x| < 5. #8. For each statement, (i) write the statement in logical form with appropriate variables and quantifiers, (ii) write the negation in logical form, and (iii) write the negation in a clearly worded unambiguous English sentence....
please do question 4 and 5 and state if the statement is true or false. please and thank you 1.1 BASIC LOGIC which net "There exits EN such that for every E nd > 1 & Why did we eaten ", bet not > Oor ">" Why didn't we change the and to an "or"? Note that the symbol wands for greater than or equal to and so the nation of i n - lisbot greater than and mot equal...
1. Consider the function h:Z+ +Z+ defined by h(n) = l{k e Z+ : k|n}l. The bars around the set mean that we are taking the size of the set. Thus h(n) is the number of positive divisors of n. (a) Make a table of values for h(n) for 1 sn < 10. Write one or two sentences describing how you found the values in the table. (b) Find the value of h(90). Explain how you found your answer. (c)...
Please show the solutions for all 4 parts! Problem 1 Let m E Z that is not the square of an integer (ie. mメ0, 1.4.9, ). Let α-Vm (so you have a失Q as mentioned above) (i) Prove the following:Qla aba: a,b Q is a subring of C, Za]a +ba: a, b E Z is a subring of Qla], and the fraction field of Z[a] is Q[a]. (3pts) (ii) Prove that Z[x]/(X2-m) Z[a] and Qx/(x2 mQ[a]. (3pts) i Let n be...
1. Anharmonic oscillator. Hydrogen bromide, 'HiBr, vibrates approximately according to a Morse potential VM(r) = Dell-e-w2De)1/2 (r-rej2 with De= 4.8 10 eV, re= 1.4 1 44Ă, and k= 408.4 N m-1. With ω,-VRA, the energies of the stationary states in a Morse potential are En (hwo) 4D ho(n+ 1/2)- (n + 1/2)2. (A) On the same graph, plot the Morse potential and the harmonic potential as a function of bond length (from 0.7 Te to 2 re).(B) Describe the differences....
Battery Identical Lightbulbs Initially, made of tungsten which has n-6e+28 e/m 3 and u-0.0018 (m/s)/(N/C). The radius of the filament is 4.1e-06 m. The capacitance of the capacitor is 0.8 F. The total length of the connecting wires is 9 cm. Before you answer the questions below, write down two correct Δν round trip (energy conservation) equations for this circuit. The equations should be general (that is, correct for all times after t-0 and not only applicable for a specific...
e (4 marks) Let m be an integer with the property that m 2 2. Consider that X1, X2,.. ., Xm are independent Binomial(n,p) random variables, where n is known and p is unknown. Note that p E (0,1). Write down the expression of the likelihood function We assume that min(x1, . . . ,xm) 〈 n and max(x1, . . . ,xm) 〉 0 5 marks) Find , and give all possible solutions to the equation dL dL -...
a) Let f : R → R be a function and CER. Definition 1. The lim+oe an A if for every e>0 there erists a M EN such that for all n 2 M we have lan - A<E Complete the following statement with out using negative words (you do not have to prove it): The lim, 10 10if R).Consider the following subsets of P: (b) Let P2-(f(t)- ao at + azt | ao, a1, a2 and Notice that Y...
Subject: Algorithm solve only part 4 and 5 please. need urgent. 1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use...