GARAAAAAAA Divided Dieiences Using the larulla Prove thek hint A- n-l (지
Exercise 9. (Submit a) a) Prove (p4) directly using inclusion-exclusion Hint: With n= pi p?... per set A; = {me [n] |P: | m} Then E (n) = N A
지↓) Assuming 자t) is band l:mited to asoHz uhat is g(L) as a Rndial Consider the following block diagram for sampling and reconstruction of a continuous-time signal s(t) sE)
For an Ideal gas, prove that L + n)。
4. Let n be a natural number (a) Prove that -2 ()= ("71). (Hint: consider the cases n 1 and n 2 2 separately.) 3 () (b) Conjecture and prove a similar expression for 3 ()? .n (c) What is
2. If L is a regular language, prove that the language 11 = { uv/ u E 1 , |v|-2) is also regular. (Hint: Can you build an NFA of L1 using an NFA of a language L? Use N, the NFA of the language L)
Problem 30. Prove that N, Z, Q and R are infinite sets. (HINT: Prove by induction on n that is f: NN then (3k N(Vj Nn)k> f(j). Then conclude that f cannot possibly be onto N. A similar strategy works for Z, gq and R as well.)
Prove that every subset of N is either finite or countable. (Hint: use the ordering of N.) Conclude from this that there is no infinite set with cardinality less than that of N.
Numerically compute the integral of (x) = 5 + sin2(x) on the interval [0,지 for n-2, 4, 8, 16, 32, and 64 equally spaced subintervals using the midpoint, trapezoidal, and Simpson 1/3 rule. Compare the results with the exact value of the integral, and determine the order of accuracy for each method based on the n = 32 and n 64 results Perform hand calculations for the n = 2 cases, but develop MATLAB programs to perform the rest of...
By using a constructive method, prove that there is a positive integer n such that n! < 2n By using an exhaustive method, prove that for each n in [1.3], nk 2n. By using a direct method, prove that for every odd integer n, n2 is odd. By using a contrapositive method, prove that for every even integer n, n2 By using a constructive method, prove that there is a positive integer n such that n!
1. Suppose that f : NR. If lim f(n+1) f(n) = L n-oo prove that lm0 S (n)/n exists and equals L 1. Suppose that f : NR. If lim f(n+1) f(n) = L n-oo prove that lm0 S (n)/n exists and equals L