Working on Set operations and Ven diagram Help needed to understand this problem: If n(A)=28, n(B)=22, n(A intersects B)=8, and n(A’ intersects B’)=18 find n(A’ union B)

Q: How many lattice paths start at (3,3) and end at (10,10)? end at (10,10) and pass through (5,7)?…

A: In a lattice paththe only movements allowed are 0,1 and 1,0 which are one step north and one step…

Q: What is the minimum number of balls that we need to draw to ensure that we get at least 3 balls…

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Q: How many shortest lattice paths start at (5, 5) and b. end at (14, 14) and pass through (8, 12)? c.…

A:

Q: 3.Two projects are proposed in the organization. Out of the 30 members, 14 members like project A,…

A:

Q: 26 Is it possible to take a walk around the city whose map is shown below, starting and ending at…

A:

Q: Paul has 20 thin rods whose lengths, in centimetres are 1, 2, 3, ..., 20. Any two rods can be…

A: paul has 20 thin rods where lengths in centimeters are 1,2,3,....,20. as we know, perimeter is the…

Q: a) Jairon needs to create a paSsword for his internet account. To simplify things, he is going to…

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

Q: Suppose we want to choose 5 objects, without replacement, from 15 distinct objects.   How many ways…

A: topic -  permutation and combination

Q: Assune that you have a committee of 12 members, made up of 3 men and 9 women. In how many ways can…

A: Given, 12 members in the committee, made up 3 men and 9 women  To find the number of ways 3 tasks be…

Q: schedule is to be made with football teams. Suppose that 7 teams need to play with three other teams…

A: It's clear from the given problem that 7 teams play against three other teams. This leads to 7…

Q: a) You are one of a team assigned to find the best locations for bus stops between North Amman bus…

A: Based on LCM of two numbers

Q: (k+1)! −1+ (k+1) ( K+1)! (k+1)! [₁ + (k+1)] = = (k+1)! (k+²) -1 (k+2)! - 1

A: Introduction: Factorial is a very important symbol in mathematics. It is always applicable to any…

Q: A box contains 5 yellow, 8 green, 11 blue, 11 purple and 15 white balls. What is the minimum number…

A: Number of yellow balls = 5 Number of green balls = 8 Number of blue balls = 11 Number of purple…

Q: You get to choose a 6 digit PIN for your new account. A restriction on the PIN is that no more than…

A: First, let's count total number of possible 6 digit codes. We can use numbers from 0-9 are 6 places.…

Q: There are 4 major roads from city x to city y and 3 major roads from city y to coty z. How many…

A:

Q: A class of 50 students opens two vacant positions for the potential president and a treasurer. How…

A: The question is based on permutation. We will use the following formula for solving the problem.…

Q: The exam has 14 questions, and the total number of marks for the exam is 100. In how many ways can…

A: Let us assume that: Pi=The point assigned to the ith question.   Given that:  Each question must…

Q: You have to do 10 homeworks (HW) of 2 different courses: 6 HW from course A, and 4 HW from course B.…

A: We have to use permutation to solve this question  Number of way r object can be arranged by taking…

Q: There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing…

A: Permutation and combination When the letter, people etc needs to be arranges in such a way in which…

Q: Alice has 10 balls (all different). First, she splits them into two piles; then she picks one of the…

A:

Q: Suppose that a climber spent four days in a camping to be well-prepared for the next climbing. For…

A: Given information:   The frequency table corresponding to the number of fruits is as given below:…

Q: Paul has 20 thin rods whose lengths, in centimetres are 1, 2, 3, ..., 20. Any two rods can be…

A: Given information: Paul has 20 thin rods whose lengths, in centimeter's are 1, 2, 3, ..., 20. We…

Q: Express (4, 10) as a set {x : |x − a| < c} for suitable a and c

A: Write the given interval in inequality form as follows: 4<x<10

Q: An operation * is defined on the set R by x * y = x +y+ 6 where x, y are elements of R. What is…

A:

Q: The intersection of sets K and L will

A: our objective is to find the intersection

Q: A checker is placed in the bottom row of a checker board as shown below. It can move diagonally…

A: This is a counting problem.. we will solve it using the approach of dynamic programming

Q: in a survey of 320 test takers, 60 students used both techniques to relax, 200 students used deep…

A: In a survey of 320 test takers, 60 students used both techniques to relax, 200 students used deep…

Q: use the union rule to answer the question.  If n left parenthesis Upper A intersect Upper B right…

A: Given,

Q: How many lattice paths start at (3,3) and (a) end at (10,10)? (b) end at (10,10) and pass through…

A:

Q: You have to do 10 homeworks (HW) of 2 different courses: 6 HW from course A, and 4 HW from course B.…

A: Given that, You have to do 10 homeworks (HW) of 2 different courses. 6 HW from course A. 4 HW from…

Q: drawer contains 17 black socks, 17 white socks, and 17 blue socks. If the light is off and Carol…

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Q: There are 10 questions in a final ėxamination for Discrete Mathematics. Each question is assigned at…

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Q: 2. Sometimes light fixtures are controlled by more than one switch. Circuits need to be designed so…

A: Given that the circuit for a light fixture controlled by more than one switch (take 3 switches),…

Q: Suppose we want to choose 6 objects, without replacement, from 8 distinct objects. (If necessary,…

A: Given data: Number of distinct objects  (n) = 8 Number of objects to choose(x) = 6

Q: Đ A is a closed set.

A: We prove by using the result that intersection of two closed set is closed.

Q: how many shortest lattice paths start at (4,4) and a. ends at (11, 11) b. end at (11, 11) and pass…

A:

Q: Room A Room B 7 Room C | Room D 6 Room E 4 Figure 1 i. He wanted to give a tour for his friend. Is…

A: 1) Yes, that is possible. He want to walk through every doorway exactly once. So, he should try this…

Q: A signal can be formed by running different colored flags up a pole, one above the other. Find the…

A:

Q: The company is celebrating the 300th national day of Norway and wants to include monetary prizes…

A: Say there are n bags available. Let  denote the first time a bag with a prize is sold. Then…

Q: The defining property of an ordered pair is that two or- dered pairs are equal if and only if their…

A: Firstly suppose that a,b=c,d i.e a,a,b=c,c,d. We have to show that a=c & b=d. There will be two…

Q: Catalina works part-time at a bakery earning $7.50 an hour. In the last five days, her time card…

A: Given: Per hour pay of Catalina = $ 7.50 Given: In the last five days, her time card shows that she…

Q: Someone has stolen an ATM card and knows that the first and last digits of the PIN are 5 and 1,…

A: The total number of digits from 0 to 9 is 10.

Q: With a short time remaining in the day, a delivery driver has time to make deliveries to 6 different…

A:

Q: in a rugby match, a tie at the end of two overtime. Leads to a shoot out with five cakes taken by…

A: GivenLeads to a shoot out with five cakes taken by each team from the center of the 22 m line. Each…

Q: How many different paths are there that reach from the top to exit 5?

A: Solution: The pascal's triangle is

Q: Let us take an example of two islands with four rivers forming the surrounding water. There are…

A: Given: An example of two islands with four rivers forming the surrounding water. To find: Whether a…

Q: Two sets A and B contains a and belements respectively. If power set of A contains 32 more elements…

A: If a set S contains n number of elements then the number of elements in its power set is 2n here…

Q: The technique of boxing in a triangle and determing its area by using rectangle and right triangle…

A: Let ABC is triangle with vertices, Ax1,y1,Bx2,y2,Cx3,y3. WhereDx1,0, Ex2,0, Fx3,0 are points on…

Q: Color list 1 Red 2 Yellow 3 White 4 Black 5 Orange. Each floor of the 4-storey building will be…

A: There are 5 colors and 4 layers.   We can paint the first layer in 5 ways.  When the first layer is…

Q: For a survey of 120 law school students, it was found that: 60 took probate law, 90 took criminal…

A: 34 students took exactly one of the courses.   The detailed solution is as follows below:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.