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

Q: @ In a G Survey the 100 out-patient who reported at a hospital one dey, it was found out that 70…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: What is the cardinality of the set of 2 x 2 matrices over N? Prove your answer.  Note: a 2 x 2…

A:

Q: Let (A, 3) be a poset, and let BC A. Prove that B has at most one greatest lower bound.

A: Let, A,<~ be a poset and B is a subset of A and a∈A. Then by the definition, a is the greatest…

Q: The Boolean sum of the variables z, y and z or their complements, that has the value 0 if and only…

A: Given x=0y=1z=1 Thus yc = 0zc = 0 We know that  a+b = 0 if and only if both a and b are zero

Q: A set of dice is called intransitive (or non-transitive) if it contains three dice, A, B, C, with…

A: There are three dice, which have the following faces: Die A= {2,2,4,4,9,9} Die B= {1,1,6,6,8,8} Die…

Q: o add into figure 1 by drawing the directional link(s) to/from the variable X7 from/to the relevant…

A:

Q: of multicolored balls contains 3yellows, blue, U1 black 5pink balls.f 3 batls ace drawn from bag…

A: Given : No. of yellow balls = 3 No. of blue balls = 4 No. of black balls =1 No. of pink balls = 5 So…

Q: Prove that at a party where there are at least two people, there are two people w know the same…

A:

Q: It was found that 33% of all diners order vegan meals and that 90% of all diners are undergraduate…

A: The following information has been given: Let us consider "V" denotes the event diner orders a…

Q: Three Carcs chawn rom are Paek Sa కజ (ande that ll club Conds Find -The probabitity Dumbered on

A: Given, three cards are drawn from a pack of 52 cards. Now, n (cards are numbered or club cards) =40

Q: 0.3 0.7 0.2 0.1 0.5 0.4 0.5 0.기 0.6 10 11 Which (if any) states are inessential? Which (if any)…

A:

Q: 4 A school has 137 math students. a) Prove that if the principal hires 8 math teachers, then at…

A: According to the given information, Number of math students in school = 137 For part (a) it is…

Q: A sukvEr OF 324 VLAN TO APPLY To A 4-YEAR UNINGestrr- 105 LAN TO AYLY TO A 2-KEAR JUNIOR COLLEGE.…

A: Given Let A→4 year        B→2 year A=324B=105A∩B=15

Q: Suppose that N+ 1 balls, of which a+b+1 are red and N-a-bare blue, are arranged in a linear order in…

A: From the given information, There are N+1 balls, of which a+b+1 are red and N-a-b are blue arranged…

Q: If ZH and LJ are supplementary in HJKL, are a) ZK and ZL necessarily supplementary also? b) ZH and…

A: Given :∠H and ∠J are supplementary…

Q: Prove that, if (a%m)=(b%m) then m| (a-b)

A:

Q: Consider the traffic flow diagram that follows, where a1, a2, a3, a4, b1, b2, b3, b4 are fixed posi-…

A: The complete solution is in given below

Q: Find the SVD of 3 A = 2 3 -2 [Hint: Work with AT]

A:

Q: Determine whether the sene SJAM 901 9U ws(nT)is absolutely ionvergent 31 in (n) n=2 conditionally…

A:

Q: 4 Compute |w using w= - 3 - 4

A: Given a vector space V over a subfield F of the complex numbers , a norm on V is a real valued…

Q: 7. Use Boolean Algebra to prove that- A.(B + C ) + A (C + B ) = A

A:

Q: Prove or disprove that if {a,} and {b,} are Cauchy and b,n # 0. Then An is Cauchy

A: If an and bn are Cauchy and bn≠0, then anbn is not Cauchy. Result used: If an and bn are Cauchy and…

Q: In Excrcises 9-18 mark each statcment True or Falsc (T/F). Justify cach answcr. 9. (T/F) If vi....…

A: As per company guidelines, we are supposed to answer only first question. Kindly ask others as…

Q: Prove A by Contradiction

A: Solution :-

Q: 1. Show that the following language is decidable, by reducing it to ECFG (which we already know is…

A:

Q: .

A:

Q: Let A = {a} and B = {{a}}. Prove that in general A + B. Thus, the presence of curly brackets is…

A:

Q: Prove that, if m | (a-b) then (a % m) = (b % m)

A: Since you have asked multiple questions we will solve the first question for you. If you want to be…

Q: (A) Compute the (infinite) discrete convolution (-2, –5, –3, –1) • (–4, –4, –5, –4).

A: Use the sum by column method to calculate the discrete convolution .                 Disclaimer:…

Q: Let m and n be two relatively prime positive naturals, and consider what naturals can be expressed…

A:

Q: Prove that if A is similar to B and B is similar to C, then A is similar to C.

A:

Q: ,- ). Show that there a 3,4

A:

Q: Prove for all m, n, and k in w, that (m⋅n)k = mk.nk.

A:

Q: Compute the Lie Symmetries for following PDES 1- ut = uxx+u² 2- ut = Uxxx + u²

A: Given:- 1) ut=uxx+u2 2) ut= uxxx+ u2

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: There are two food carts serving food at a local park. At any given time, Let A denote the number of…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: an be cauchy, prove why a subsequence of (an) must also be cauchy.

A:

Q: Let a and b be two elements in a lattice (A, ≤). Show that a ˄ b ˂ a and a ˄ b ˂ b if and only if a…

A: Suppose that a∧b<a and a∧b<b. To show that a and b are incomparable assume the contrary that a…

Q: 2. Prove thatN is the smallest inductive subset of R:

A: We can prove this by proving property of induction

Q: 2. Show that if u is a SC

A: Given, if u is a solution of                          ∇2u+D(x, y)∂u∂x+E(x, y)∂u∂x=-F(x, y) in D with…

Q: Prove, without using Theorem 1.12 or copying the proof, that for all a, b ∈ Q with a < b, there…

A:

Q: What is the general solution for the recurrence relation t,n = 13tn-1 – 36tn-2 ? %3D (1) tn =…

A:

Q: Let x, x2, ....X10 be distinct Boolean random variables that are inputs into some logical circuit.…

A:

Q: In a study of pain relievers, 25 people were given product A, and 16 experienced relief. In the same…

A: According to the study of pain relievers 25 people were given product A, and 16 were relieved.  So…

Q: Suppose that every student in a discrete mathematics class of 25 students is a freshman, a…

A:

Q: Use the rules of inference to show that if 3x(M(x) ^ P(x)) and Vx(K(x) → ¬M(x)) are true, then…

A: Introduction: When an argument is given in quantified form, the rules of inference are also used.…

Q: Show that if A and B are both n × n, then (a) det(AT BT ) = det(A) det(BT ); (b) det(AT BT ) =…

A: Given A and B are n×n matrix.

Q: If v ∈ A and v is an upper bound of A, then v = sup A

A: Given: If v ∈ A and v is an upper bound of A, then v = sup A

Statements and Logic

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