) shade (ANB) ule-A)

Q: How many subsets of the set {1,2,3,4,5,6,7,8} have cardinality 3 or less?

A: Here we need to find how many subsets of the set A={1, 2,3,4,5,6,7,8} have cardinality 3 or less so…

Q: define a set of which both {1,3,4} and {0,3,5} are subsets find such a set with the smallest…

A: We have to find the set with smallest possible number of elements which both {1,3,4} and {0,3,5} are…

Q: Let set A be the set of face cards and B be the set of all spades in a regular deck of cards. State…

A: There are 12 face cards in a regular deck of cards and 13 spades in a regular deck of cards. Set A:…

Q: If AnB is pathwise connected set.  then A and B are:  a. Pathwise connected sets b. Not pathwise…

A: Pathwise connected means any two points in that set can be join by a continuous function. Roughly…

Q: {(x,a),(x,b),(x,c), (y,a),(y,b),(y,c)} is the Cartesian product AXB of two sets given as A = {x,y} B…

A: Let A and B are two sets. Cartesian product of A and B will be denoted by  A×B                A×B…

Q: Find the dimension of the set S= {(2, 4), (4, 8)}?

A: The dimension of the set S can be find out by finding the linearly independent vectors in it.…

Q: => find fundamental set of Se yo=-3x²e-3x ZR 7:

A: We have to find the fundamental set of solution.

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

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Q: The set of elements in (-, 9) or (-, 12) or in both sets is .

A: The sets are (-∞,9) , (-∞,12)

Q: Show that each pair of sets is equivalent by using a one to one correspondence. {1,2,3,4,. . . .} is…

A:

Q: Let A=span(u,v) and B=span(u,v,w). Which statement is true? - A ≠ B and that is all you can say…

A: Let A=span(u,v) and B=span(u,v,w).

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: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

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Q: A set which has ho element is said to be

A: A set with no elements = { }

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: Assume that A={A,B,C} and B={5,4,1,9,6} A code consists of 2 different symbols selected from X…

A: Given: Assuming X={A,B,C} and Y={5,4,1,9,6}. A code consists of 2 different symbols selected from X…

Q: Let A = {1,2, 3} be a set. Then the Cartesian product Ax A = {1,4, 9}.

A: In the given question we have to tell about the statement s.t are they true or false. (1) the given…

Q: Give an examf there exists pairwi- are no te:- Explai

A: In this question we have to find different integers a,b,c,d such that there exist no positive…

Q: two example of open set in R, closed set in R, and the closure of that set

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Q: In the class of 50 students, 24 like Arabic, 21 like English and 18 like Mathematics 6 like Arabic…

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Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: 1. Give at least 5 pairs of numbers a and b. For each of those pairs find at least 10 elements of…

A: We need to find at least 5 pairs of numbers a and b. For each of those pairs  at least 10 elements…

Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

Q: Prove that [0,1] has the same cardinal number as [0,2] U[7,9].

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Q: 8. have a job}, draw a Venn diagram relating the two sets, giver that the universal set U={Human…

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Q: Show that the N and the set {1,3,7, 15, 31, . . } have the same cardinalit

A: To show N and the set S= {1,3,7,15,31...} have the same cardinality, we need to show there is a…

Q: The Cartesian product of two sets containing five elements each has a cardinality of * O 16 Cannot…

A: Consider the given two sets which have each cardinality 5 Let set A=a,b,c,d,e and B=1,2,3,4,5

Q: Define a set of which both {1, 3, 4} and {0, 3, 5} are subsets. Find such a set with the smallest…

A: {0,1,3,4,5} is the smallest set that contains {1, 3, 4} and {0, 3, 5} as sub-sets.

Q: How

A:

Q: A product code consists of a string of 4 different letters selected from the set {S,T,U,V,W,X}. How…

A: The number of ways to arrange r objects selected from n distinct objects is given by the permutation…

Q: Given A={2,4,6,8} and B={1,3,5,6}. What is the cardinality of the union of set A and B?

A: Number of element in A union B is 7. Actually in sets we are not writing same element in twice.

Q: Is the set (9, 20] under usual order ≤ well-ordered? Why?

A: We need to determine the set (9 , 20] under usual order is well - ordered or not. We know that , a…

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A: Consider the given set A = {a, b, c}. A proper subset of a set A is a subset of A that is not equal…

Q: how many subsets of {0,1 ....,9} have cardinality 4 or more?

A:

Q: Suppose that set A has 17 elements, set B has 10 elements, and their union has 18 elements. If the…

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Q: a) Find the cardinal number of the set of letters in the word "MALAYALAM" b) If A = {5, 7, 8,…

A: Cardinal number of a set A is the number of elements of the set A.

Q: Specify the sets by roster, (a) (Even counting numbers less than 14) (b) (Positive muitiples of 7)…

A: To simply the sets in roaster form

Q: How many elements are in the set {0, {0}}?

A:

Q: Let U be the universal set of all the letters in the English alphabet. What is the complement of the…

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Q: specify the set by roster distinct letters in the word (mathematics)

A: Given that

Q: A set contains fourteen elements. How many subsets can be formed from this​ set?

A: Given that A set contains fourteen elements. To find How many subsets can be formed from this​ set

Q: A set has 9 elements. How many subsets of S are there with at most 2 elements?

A: Given,            A set has 9 elements. Subsets of S are there with at most 2 elements.

Q: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

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Q: Assume that X={A,F,H,D,C} and Y={5,9,4,2,3}. A code consists of 4 different symbols selected from X…

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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: We form the intersection of two sets. We know that one of them has n elements and the other has m…

A: Given : A=n , B=m To Find : Cardinality of A∩B

Q: what is the cardinal number of the set {1, 3, 7, 4, 22, 16, 12}? Where denotes the set of all…

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Q: 5. Consider the generic Venn diagram for three sets. (a) Add one figure showing a fourth set D. (b)…

A: The generic Venn diagram is:

Q: How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear…

A: To find number of ways are there to arrange the 26 letters of the alphabet so that no pair of vowels…

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”.