List all the elements of the following sets :(i) A = {x : x is an odd natural number}(ii) C = {x : x is an integer, x2 ≤ 4}        (iii) D = {x : x is a letter in the word “LOYAL”}                                                 (iv) E = {x : x is a month of a year not having 31 days}                                      (v) F = {x : x is a consonant in the English alphabet which precedes k }.

Q: How many distinct ten-digit passwords are possible if you must use at least one 26 lower case letter…

A: Given: you must use at least one 26 lower case letter from {a, b, . . . , z}, at least one 26 upper…

Q: Suppose that a password for a computer system must have at least 6, but no more than 9 characters,…

A: Given,  a password for a computer system must have at least 6, but no more than 9 characters, where…

Q: 2) Each type of machine part made in a factory is stamped with a code of the form…

A: We can use :- 26 letters, 10 digits, 10 digits (as digits can be repeated)   Total number of…

Q: 2. What is the number of k-digit strings one can form over an n-element alphabet if (a) there are no…

A:

Q: Suppose we want to choose 4 objects, without replacement, from 18 distinct objects. (a) How many…

A: Permutations and combinations

Q: At a certain company, passwords must be from 4-6 symbols long and composed from the 26 uppercase…

A: Let us consider there n number of objects, and r to be chosen such that repetition is allowed; then,…

Q: Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are Math books, 3 are…

A: Given:- total books =10 maths books =4 Chemistry books =3 history books =2 song lyric book =1

Q: What is the best choice for the cardinality of the set of all finite subsets of N (N = { 0, 1, 2,…

A: Concept : The cardinality of the set is the measure of the no. of elements in the set . for, finite…

Q: How many different passwords are there that contain only digits and lower-case letters and satisfy…

A: Given, no. of digtis = 10  (0 to 9) no. of letters = 26  (a to z) Total = 36 (iii) Password must…

Q: If ten integers are chosen from between 0 and 21 exclusive, must at least one of them be even?…

A: Pigeon hole principle states that if n objects are put in to m containers with n>m then at least…

Q: A large corporation classifies its many divisions by their performance in the preceding year. Let P…

A:

Q: 2. If a set X has n elements, how many elements are in the power set P(X), we exclude the empty set…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: What are the number of distinct subsets and number of distinct proper subsets for {a,b,c,d,e,f}?

A: The set contains 6 elements . We know that number of subsets of set of n elements is 2^n. So given…

Q: Investigate and illustrate the cardinality of the sets of odd numbers, ?, and ℤ, which properly…

A:

Q: A box contains 15 balls in which seven are green and eight are yellow. If five balls must be drawn…

A: It is given that Number of green balls = 7 Number of yellow balls = 8 Total number of balls = 15…

Q: If seven integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? Why?

A:

Q: Suppose we want to choose 7 objects, without replacement, from 9 distinct objects. (a) How many ways…

A:

Q: What is the minimum number of students required in a discrete mathematics class to be sure that at…

A: We solve the given problem in next step.

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: 1. The set of counting numbers greater than -1 and less than 9 2. The set of integers satisfying X -…

A: Roster method is to express the set in terms of flower brackets, for example to write the set of…

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: A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the…

A:

Q: Suppose we want to choose 6 objects, without replacement, from 10 distinct objects. (a) How many…

A: We can find answer to both the question as below

Q: How many unordered sets are possible that contain three objects chosen from seven?

A: Number of unordered sets that contain three objects chosen from seven = 7C3

Q: Suppose A₁, A2, ..., A30 are thirty sets each having 5 elements and B₁, B₂, ..., B₁ are n sets each…

A: Given that A1, A2, . . ., A30 are thirty sets each having 5 elements and B1, B2, . . ., Bn  are 'n'…

Q: Let U be set of letters in the English alphabet, A be the set of distinct letters in the word…

A: Question in 2 is not clear what is True or False.

Q: 1. How many distinguishable ways can the letters of the word MILLIMICRON be arranged in order?

A: According to our guidelines, We can answer only first question.

Q: ct proper subsets are there of the set N = {3, 43}?

A: The number of elements in the set are 2 ( which are 3, 43)

Q: Each character in a password of length six can be any uppercase letter from A-Z or any symbol from…

A:

Q: Suppose we want to choose 5 objects, without replacement, from 15 distinct objects. 1) How many…

A: Provided information is ; number of objects(n) =15 For Case 1] : if the order of the choices is…

Q: 1. How many words of length 5 are there on the set {A, B,C, D} which do NOT contain the string…

A: As per our honor code, we are authorized to answer only one question at a moment. As you have not…

Q: Standard license plates for passenger vehicles in California are of the form NMLMXXX where N is any…

A: GivenThe form of Standard License plates = NMLMXXXN = digit except 0X = any digitL = Upper case…

Q: How many strings of ten lowercase letters from the English alphabet contain the lette consecutive…

A: String contains total 10 lowercase letters

Q: 1 A class of 40 students was each required having three textbooks in each of Economics, Mathematics.…

A: Topic:- ven diagram

Q: so the S and T remain next to each other (though not necessarily in that order, so ST or TS are both…

A: Consider as S and T as one letter. So now the total number of English alphabet which needed to…

Q: A. How many 3-digit numbers can be formed from the set of decimal digits if the numbers formed are…

A: Answer is given below:

Q: How many strings of 7 decimal digits are there, such that at least one of the digit is odd?

A: There are total 10 decimal digits, among which 5 are odd. Since repetition of digits is allowed,…

Q: { n ∣ n ∈ N and 405 < n ≤ 437} H has --------  subsets. H has--------  proper subse

A: It is given that ,  H=n|n ∈N and 405 &lt; n ≤437we have to find , H has ................. subsets.H…

Q: 2. If the set S in each part is finite, write down S. i. S={primes) ii. S= (even primes) iii. S=…

A: 2. Given that S in each part is finite . i. S={Primes}. S={2,3,5...}. This set has infinitely many…

Q: How many unordered sets are there of two items chosen from eight?

A: To find unordered sets of two items chosen from eight. Number of unordered sets r chosen from n is…

Q: Suppose we want to choose 6 objects, without replacement, from 9 distinct objects. (a) If the order…

A: Solve

Q: 3. Find the number of subsets for set containing 3 elements.

A: Given set  containing 3 element

Q: 2. Suppose that a password for a computer system must have at least 8, but no more than 12,…

A: As Dr. S. N. De said "A permutation of a set is defined as an arrangement of its members into a…

Q: 23 In a plane of 160 passengers, the airline has provided 48 meals of chicken rice, 78 meals of…

A: A Venn diagram is an illustration that uses circles to show the relationships among things or finite…

Q: In a drawer, there are eight blue socks, six green socks, and twelve black socks. What is the…

A:

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

A: Given data: The total numbers of objects are n=15. The numbers of objects choose is r=5. (a) Write…

Q: Television and radio stations use four call letters starting with W or​ K, such as WXYZ or KRLD.…

A: the total number of alphabets between A to P is 16.

Q: How many distinct proper subsets are there of the set N = {4, 49, 63, 12, 36, 55}?

A: A proper subset is subset which is not the whole set itself.    There are 2n subsets of a set where…

Q: Solve the following problems using a Venn Diagram. 2. In a certain university 2,191 students are…

A: First, let's draw a Venn Diagram using the given details.

Q: i. How many three-digit phone prefixes that are used to represent a particular geographic area (such…

A: here, AS PER GUIDELINES  I HAVE CALCUALTED FIRST MAIN  QUESTION  HERE USE COMBINATION , TOTAL…

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”.