Bartle The Elements of Integration and Lebesgue Measure: 4.R. If fe M*(X, X) and is due < +00, then the set N = {xe X: f(x) > 0} is o-finite (that is, there exists a sequence (Fa) in X such that N CU Fn and u(F.) < too).
Consider the set of all functions from {1, 2, ..., m} to {1, 2, ..., n}, where n > m. If a function is chosen from this set at random, what is the probability that it will be strictly increasing? (A) (n)/m”. (B) (%)/nm. () (min-1)/m". (D) (matema!)/n".
1. (9pts) Suppose A is a set with m elements and B is a set with n elements. a. How many relations are there from A to B? Explain b. How many functions are there from A to B? Explain C. How many relations from A to itself are reflexive? Explain
Write down the elements of the following: • A = {x + Z: c2 < 2}, 4. P(P(A1-{-1})),
2. Suppose P and Q are positive odd integers such that (PQ)-1. Prove that Qm] Pn] P-1 0-1 0<m<P/2 0<n
3.4. Suppose a and b are positive integers. Prove that, if aſb, then a < b.
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
3.13 Determine the DTFT of the two-sided sequence y[n] = a1",jal < 1.
Let U ? Rmxn. Prove that if UTI-In, then n < m.
H = {b | b € N and 120 < b < 114) Use the roster method to list the elements in the set H. Points possible: 2 This is attempt 1 of 3. Submit