Calculate (n| ² | m) and (m | 4 | n) in the N-representation; | n) and | m) are harmonic oscillator states.

A state is said to be recurrent if there exists state j that is reachable from i but the the state i is not reachable from state j Select one: True False

4) Use the given lattice to find all pairs of elements that generate Dg. (There are 12 pairs) D8 (s,r?) (r) (rs,r2) (s) (r?s) ip2j (rs) mel lainono onil sd to

Exercise 1.2.4. Produce an infinite collection of sets A₁, A2, A3, ... with the property that every A, has an infinite number of elements, A, A₁ = 0 for all i ‡ j, and U₁₁ A₁ = N.

The lattice points (a, b) and (m, n) are mutually visible if and only if a -m and b - n are relatively prime.

discrete math hw

A single card is drawn randomly (with replacement) from 52-card deck. Let A denotes that the card is red; B denotes the card is a face card, and C denotes that it is King (K). a) Find P (A), P (B) , P (C) b) P (A|B), and P(C|B)              means conditional c) Prove the dependency/independency of (A & B) and ( B & C) Note: There are 12 face cards, 4 kings, 26 red cards and 26 black cards

Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than 15 from w.

Exercise 1. Let S be a set with elements. For any integer k < n, let I denote the set of all subsets of S with at most k elements. Show that (S, It) is a matroid. (It is referred to as the uniform matroid U (n, k)).