Suppose chips are randomly drawn from a bag, and each chip is labeled with either 1, 2, 3, 4, 5, 6, 7, 8 or 9. Let E = "choose an odd number" and F = "choose a number less than or equal to 7". What is P(E ∩∩ F)?  Group of answer choices 3/9 4/9 5/9 5/10 None of the above

Q: 2. Let A Ø. If A has exactly n elements, then A has exactly 2" subsets, Vn € N.

A: A is non empty subset of n elements ,then A has exactly 2n subsets,∀n∈ℕ.

Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: Let A and (A, n2 1) be subsets of 2 An - A as n → 00 =P(A,) P(A). as n 0o,

A: The given question is related with probability. Given that A and An , n≥1 are subsets of Ω . We have…

Q: (iv) The power set P(C) of C by listing down the elements directly.

A:

Q: a Which of he pocess e satoay? that in some cases you may not be able to get an eact exresin.In…

A: a) Note that Therefore Yk has a pmf of a Poisson random variable, which implies that it is a…

Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2, express a, in terms of n.

A:

Q: In each of (a)-(f), answer the following questions: Is A C B? Is BC A? Is either A or Ba proper…

A: Answer is in following steps.

Q: O Show that if A is finite, then P (A) is finite.

A:

Q: For Aand B subsets of formal A x CBU C) is a se t x iprovide subset

A:

Q: (c) Prove that if A and B are finite sets, then A B is finite and A B| = |B|Al. (Hint: Use induction…

A: For (c), We are given that if A and B are finite sets. So, let |A| = m and |B| = n. Now, we need to…

Q: Represent in the Argand Diagram all such z for which |z + 13| < 15

A:

Q: Prove that if r <s < n, then P(n , s) is divisible by P(n,r).

A: Given: r≤s≤n Therefore, n-r≥n-s So we can write n-r! = n-rn-r-1n-r-2...n-sn-s-1n-s-2...1 n-r! =…

Q: Last week, there were several types of animals at a local animal shelter. Let U be the set of the…

A: The intersection of events is the common elements of those events. The complement of an event is all…

Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

A:

Q: a. Show that if a, b, c, de Zwith a +b√2 = c+d√2, then a = c and b=d. You may use, without proof,…

A:

Q: 2. Let e = |E, e2 = |E2, d = |D| be non-zero cardinal numbers. Prove: If e <e then ef <e.

A: Given: e1=E1, e2=E2, d=D are non-zero cardinal numbers. To Prove: If e1≤e2 then e1d≤e2d.

Q: 9. Give a proof by contradiction to show if A and B are sets, then A N (BN A') = {}.

A: Suppose A and B are sets.

Q: An alarm system has three different control panels in three different locations. To enable the…

A: Three different control panels of alarm are P,Q,R. It is given that system will enable(start…

Q: If X(z) = In(z - 2), then what's x(k) а. O b. ak O C. -ak / k d. others е. ak / k

A: Z transform and inverse Z transform

Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

A:

Q: Suppose chips are randomly drawn from a bag, and each chip is labeled with either 1, 2, 3, 4, 5, 6,…

A: S={1, 2, 3, 4, 5, 6, 7, 8, 9} n(S) = 9 E = odd number = {1,3,5,7,9} n(E) = 5

Q: 3. Show that the following refinement is correct (for any g, S, and S,): {-g}; if g then S, else S2…

A: Given refinement is: ~g; if g then S1 else S2. Here ~g implies the negation part of g. That is the…

Q: Prove that if r < s < n, then P(n, s) is divisible by P(n.r).

A: Use the formula of permutation

Q: (e) There exist subsets A and B of N such that (A-B) n (ANB) = TRUE FALSE

A:

Q: If A is nonsingular n*n then det(A )= det(A) Select one: O True O False

A: we know the property of the determinant is  det(A-1) = 1det(A) given A is non singular

Q: Given E denote the set of even integers and O denote the set of odd integers. Let Z denote the set…

A: Given E=Set of even integers and O=set of odd integers And Z is the set of all integers. We have to…

Q: *prove that for . P+2+3+... +n° = 2 n=!,2,3,

A:

Q: Let (2,+) be agroup of integers and cn) be acyclic Subgraup of C(2,+), Then one of the following is…

A:

Q: 1. Let, a1 = 7 and for n > 2, an = " express a, in terms of n.

A:

Q: If n is not a poime then there exist Some ab€ 7h Such that ab # Itnk fox all

A: Definition: A number which can not be factored as product of two numbers other than the number…

Q: Prove that any group of 20 people will contain at least one pair of people with the same amount of…

A: We will use Pigeonhole Principle: If n + 1 objects are placed in n boxes, then one at least one box…

Q: Find the number of elements in S1 U S2 U S3 if there are 200 elements in S1, 500 elements in S2, and…

A: Formula: The number of elements in the union of three sets A, B and C is:…

Q: Let {0, 1}N = {(a, a1, a2, . ..) : an = 0 or 1, n E N}. • Construct a 1-1 correspondence between {0,…

A: let 0,1N=a0,a1,a2,....:an=0 or 1, n∈ℕ (i) construct a 1-1 correspondence between 0,1ℕ and all the…

Q: Let A = a22 Show that if d = a¡|a» – A2jɑ12 # 0, then 1 A- = a22 -a12

A:

Q: The five most common words appearing in spam emails are shipping!  today! here! available, and…

A: Probability of an event gives the chances of event happening. The probability value can be from 0 to…

Q: We have a deck of cards. In this deck we have cards of the four different suits (clubs, diamonds,…

A: Sample space gives all the possible outcomes of an experiment. For example, tossing a coin is an…

Q: (d) utive but no two X's can be consecutive? How many permutations are there, if all three of the…

A:

Q: 4. Let M = {Civic, Corolla, Altima} and S = {Coupe, Sedan} List the elements of M x S.

A: Let M=Civic, Corolla, Altima and S=Coupe, Sedan

Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

A: It is mentioned that 1 in every 10 messages is spam. Hence, the probability that the message is spam…

Q: A study by Forbes indicated that the five most common words appearing in spam emails are shipping!,…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: 9. Which of the following is true: * N.E. always exist N. E. exist and unique neither necessarily…

A: It is an important part of statistics . It is widely used .

Q: Suppose A is open. Consider the following statements: (i) If finitely many points are removed from…

A: Given: A is open (i)If finitely many points are removed from A, then A is still open. (ii) If…

Q: If X(z) = In(z - 2), then what's x(k) a. -ak / k b. -ak С. aк d. others e. ak /k

A: Inverse Z transform found using multiplication by k property

Q: (The "harem problem") Let B be a set of boys, and suppose that each boy in B wishes to marry more…

A:

Q: he five most common words appearing in spam emails are shipping!, today!, here!, available, and…

A: I have provided solutions for first 3parts...as per Bartleby guideline!

Q: If A = {x E N x is odd, x <,7pw many SUBSETS of Acontain no even numbers?

A: If a set contains ‘n’ elements, then the number of subsets of the set is 2n.

Q: Suppose we randomly select a subset of positive integers. How large must the subset be, if we want…

A: The Pigeonhole Principle:  If there are p+1 or more pigeons, need to distribute among p pigeonholes,…

Q: If X(z) = In(z - 2), then what's x(k O a. -ak O b. ak O c. -ak /k O d. others Oe. ak / k O O

A: Given that X(z) = ln(z - 2) We have to find the value of X(k).

Q: Let P:I am in Muscat and Q: I love football. Then Q→P is given by O lam in Muscat then I love…

A: According to the statement. If I love football then I am in Muscat.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.