Suppose that {An, n ≥ 1} are subsets of 2 with P(An) = 0 for all n. Show that PU An n=1 = 0.

Q: 22] calculate the number of combination and permutation of, 5 distinct objects taken 2 at time?

A:

Q: Let A = {4n^2 + 1|n ∈ Z}. Show that A is a subset of Z but not equal.

A:

Q: Suppose X ∼ Binom(n, p). Show that E[X] = np.

A: Suppose Its probability mass function is defined as,Where,

Q: 10. Prove that (n) ≤ n/2 for n ≥ 8.

A: To prove that π(n) ≤ n/2 for n ≥ 8, where π(n) represents the number of prime numbers less than or…

Q: find the amount of odd three-digit numbers that can be created. (

A: here given digits are  [0, 1, 2, 3, 4, 5, 6]. so there are total 7 digits . here use counting…

Q: If S:= { / N - ¼/m : N,MEN, find wfs and sup 5

A:

Q: 3.5. Let n E N. Prove that if n + ÷ < 2, then n² + n2 <4.

A:

Q: Let R = [1, 2] × [1, 2]. Compute ye*"dA. R

A:

Q: Let S = {1,2,3,4, 5}, G = {(1),(123), (132)}. For each element %3D a e S, find stabc(a) and orbg(a)

A:

Q: Alireza will take IE 4301 next semester and attend EVERY class in person. He will wear a mask to the…

A: Solution

Q: Let Sy := {1-(-1):NEN. Find iNf Sy and sup Sy

A:

Q: Prove ImA = A = Aln if A is m X n

A: Given: A be m*n matrix

Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container.  And total (35+5+3)=43…

Q: An urn contains m number of red balls and n number of white balls. Two balls are selected without…

A: Solution-: We have given there are 'm' number of red balls and 'n' number of white balls We want to…

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

A:

Q: uppose that S is the set of successful students in a classroom, and that F stands for the set of…

A: Given that expression we have to find the value of

Q: Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 72 percent order a soft…

A: Given information- Percentage of the customers order a square pizza = 0.50 Percentage of customers…

Q: Let n be an element in Z. Prove that 5|n^2 if and only if 5|n.

A: If n be an element in Z. We have to prove that 5|n^2 if and only if 5|n.

Q: A container contains 50 green​ tokens, 15 blue​ tokens, and 4 red tokens. Two tokens are randomly…

A: The container contains 50 green tokens, 15 blue tokens and 4 red tokens. So, there are 50 green…

Q: Q9) In University of California among the placement cell, P(students getting placed )=2n/9,…

A: P(students getting placed)=P(students not getting placed)=

Q: Prove that there exists an n ∈ N such that 7 | (3^n − 1).

A:

Q: Let A = {4n^2 + 1 | n ∈ Z}. Show that the size of A is equal to the size of Z≥0. Z≥0 is the set of…

A: A set A is said to be countable  if there is a bijective map between A and set of natural numbers .…