(a) The domain is a group of people. Person z is related to person y under relation M if r and y have the same favorite color. You can assume that there is at least one pair in the group, r and y, such that rMy. (b) The domain is the set of all integers. rEy if x + y is even. An integer z is even if z = 2k for some integer k.

Q: Two equalence classes are either disjoint or identically.

A:

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: In this group of problems, you are given two statements, A and B: determine whether one statement…

A:

Q: Find the linear approximation of the function g(x) = V1 + x at a = 0. g(x) = Use it to approximate…

A: The function . To Find:a) Linear approximation.b) Approximate .c) Approximate .d) Graph the function…

Q: 6. The sets A and B are defined as: A = {2, 5, 7} B = {*, +} (a) Express the set A x B in roster…

A:

Q: (4) Pick another language and let the relation ♡ mean “this number written out in [your language]…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: In the Axiom Systems section of the Background chapter (1.6), a binary relation <on a nonempty set X…

A: Given X is a set consisting of 64 teams.  Let ⩽ be the relation on X such that for a,b∈X, a≤b…

Q: {(a, b) acb, a and b are finite set of integers}

A:

Q: A group of 10 friends went on a tour in Netherland. For their Amsterdam tour, each of them had to…

A: Let the A denote the set friends and set B denote the places to be visited. Therefore, cardinalities…

Q: Activity 7.2. Even if we omit the negatives, the real numbers fail to satisfy the well-ordering…

A: Given that the set R+ of all positive real numbers fails to be well ordered.

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: Uist all subsets of the set C-(1, 2, 3).

A:

Q: . The sets A, B, C are given by A = {0, 1,2}, B = {a,b) and C= {b,c,d). (a) Find A x B. (b) Find (A…

A: A=0,1,2B=a,bC=b,c,d Remember : A×B=a,b|a∈A, b∈B

Q: In this group of problems, you are given two statements, A and B: determine whether one statement…

A: Solution

Q: Let A = {1,2,3,4,5,6}, how many different relations are there on a set A?

A: First, we need to know definition  of the Cartesian Product of a set is with itself. The Cartesian…

Q: and B = {Thaddeus, Peter} be the set of male members. Let R be the relation between the sets A and B…

A:

Q: Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - U B, = N(A – B„,).…

A: Suppose that A is a set and Bnn∈I is an indexed family of sets. Then we have to prove that…

Q: Let A and B be any two sets. A binary relation from A to B is i. CAXB ii. SANB CAUB Non of these…

A: Firstly we define binary relation from set A to set B, and then conclude the answer.

Q: If {{1, 3, 5}, {2, 4}} is a partition of the set A = {1, 2, 3, 4, 5}, determine the corresponding…

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Q: 2.) Suppose A is a set with 4 elements and B is a set with 3 elements. How many relations are there…

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Q: For "x is in A intersect B" give an equivalent statement that uses "x is in A"  and "x is in B".…

A: We the following operators,  ∈ - "is in"&amp; - "and"

Q: 4. Let A = {a,b), B = {1,2], and C= {1,2,3), and see Definitions 2.2.4 and 2.2.7. (a) List the…

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Q: (10) Prove that P(A)n P(B) is equal to P(An B) for any sets A and B. What can we say if the…

A:

Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: GIve a simple example of the Well Ordering Principle of Integers

A: We have to explain the Well Ordering Principle of Integers using an example.

Q: 3. Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3,…

A:

Q: TRUE (c) The union of two sets, A and B, is the set of all elements in A and B. FALSE

A: We have to say whether it is true or not " The union of two sets A and B is the set of all elements…

Q: Let ai = [250] -10 and a2 = h [4] The set {a1, a2} will span R² unless h = (If there are no values…

A:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.