Consider the poset ({2, 4, 5, 10, 20}. |). What are the maximal elements, the minimal elements, the greatest element, and the least element of the poset? Maximal: 20; Minimal: 2; Greatest: 20; Least: none Maximal: 20; Minimal: 2, 5; Greatest: 20; Least: 2 Maximal: 20; Minimal: 2; Greatest: 20; Least: 2 Maximal: 20; Minimal: 2, 5; Greatest: 20; Least: none

Q: What is the domain of the following {(3, 4), (9,1), (10, 5), (2,15), (8, 4)}

A: Domain : Domain consist of all input values shown in x axis.

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: Let A={1,2,3,4,6,9,12,18}, then the set of maximal element is: .a {12,18} .b None {12} .d {18}

A: Given a statement

Q: Let U = {3, 4, 5, 6, 7, 8, 9, 10},  A = {4, 6, 8},  B = {3, 4, 7, 10}, and C = {3, 5, 7} . Find the…

A: It is given, U= {3,4,5,6,7,8,9,10}.

Q: Cavity Candies mass produces an assortment of hard candies, consisting of three flavors: cinnamon,…

A: Solution:

Q: Is (R,#) a poset? If it is a poset, is it a total order? (R is the set of all real numbers)

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Q: Let n, m 2 3. Find the number of 3n-element multi-subsets of the multi-set A = {n.a1, n.ag,..,n.am}…

A: Consider the given information.

Q: Q. 02: (a) Verify the commutative propernties of union and Intersection with help of A = (1,2,3,4),…

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Q: Which of the following sets of connectives are expressively adequate? →, ¬, A →, +, V 7,V ^, V

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Q: Roster form: G = {3, 6, 9, 12, 15, 18, 21, …} What is  the Set Builder form?

A: There are 2 ways of representing a set.  Roster form Set Builder form In roster form , all the…

Q: Let A = {1,2} and B = {3, 4}. (a) Find A x B (b) How many subsets Ax B of size 2 are there? List…

A: Given that A= {1, 2} and B= {3, 4}A x B is the cartesian product

Q: work out the problems refering to the sets:

A: Since there is no problem then I will just describe the sets base on the Universal set.(Note: this…

Q: Which of the following is the correct representation of A = (2,4,8,16,32,. } in set builder…

A: A detailed solution is given below

Q: If a set contains 4 elements then its power set will contain?

A: Here  Set Contains 4 Elements So For n elements  It's Number of powerset =(2^n)

Q: Let  U = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16},   A = {7, 9, 11, 13, 15},   B = {8, 10, 12, 14,…

A: Given the universal set is U=7, 8, 9, 10, 11, 12, 13, 14, 15, 16. The sets A, B and C are as…

Q: In a group of people, 68 people can speak English, 45 people can speak in Arabic and 19 people can…

A: It is given that 68 people can speak English, 45 people can speak Arabic and 19 people can speak…

Q: Which of the following is NOT a subset of 2 {a,b} x {a,b} ☐ ({a}, a) (a, {a}) ({a,b}, {a,b}) ☐ ({a},…

A: In set theory, a subset relationship denotes that every element of one set is also an element of…

Q: Q4) Let A = {1,2,3,4} be the given set. Find 1. п(Р(A)) 2. Write power set, P(A) 3. Write a class…

A: Given set is  A={1,2,3,4}

Q: Find all subsets of {{a}, {a,b},{4}}.

A: Topic- Subsets of a set We are given a set a,a,b,∅

Q: Let N={1,2,3,4,...}. Let P(x,y) be the predicate that x is less than or equal to y^2

A: (d) S = {1, 2, 3, 4, 5, 6, 7, 8, 9} (e) T = {3,4,5,6,......} (f) R = {} (empty set)Explanation:(d)…

Q: A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A: From the given information, The universal set U with 66 elements has been partitioned into three…

Q: What is the domain of the following: {(3,4), (9,1), (10, 5), (2, 15), (8, 4)}

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Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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Q: 4. Let A = {a, b, c, d, e, f, g, h, i, j, k}. (a) How many subsets of A contain exactly 8 distinct…

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Q: Find the number of subsets of the given set. (x|xEN and 7<x<12}

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Q: What is the domain of the following: {(3,4), (9, 1), (10, 5), (2, 15), (8, 4)} O {3, 4,9, 1, 10, 5,…

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Q: Prove. Power set of a null set is empty.

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Q: How many subsets of a set with 64 elements have more than two elements

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Q: Consider two sets A and B such that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Find the set C…

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Q: For the poset, R = ( { 1, 2, 3, 5, 10, 15, 20, 25, 30, 35, 50, 70 }, | ):   Draw the Hasse digrams…

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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.

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.