universal set U consists of 18 elements. If sets A, B, and C are proper subsets of U a n(A U B) n(A' UC) n(ANB)' n(A U B) = 15 implify your answer.) n(A' U C) = D implify your answer.)

Q: Define a smallest possible set of which both {1,3,5} and {0, 3,4 } are subsets.

A: The subsets given are {1, 3, 5} and {0, 3, 4}.

Q: Let S be a set with |S|=6 . In how many ways can we partition the set S into three non-empty parts?

A: Answer:   3   Here    |S| = 6 So there are total 11 possible partitions which are 6 5+1 4+2 3+3…

Q: if A ={x,{y},1,2,3,{2,3},{3}}      {} a proper subset of A      true or false

A: The problem is concerned with the nature of the empty set. The specific question is whether the…

Q: Let UU be the universal set, where: U={1,2,3,4,5,6,7,8,9}U={1,2,3,4,5,6,7,8,9} Let sets A, B, and C…

A: Given that               U={1,2,3,4,5,6,7,8,9} Let sets A, B, and C be subsets of U, where:…

Q: 9. Consider the 8-elements set A = {a, b, c, d, e, ƒ, g, h} . How many subsets of set A have 4…

A: Solution

Q: Prove or disprove: For all sets A and B, An(AUB)

A: We have to prove or disprove , for all sets A and B A∩(A∪B)=A.

Q: Let S be the universal set, where: S = {1, 2, 3, .., 23, 24, 25} >....

A: Given…

Q: Assume that the set S has 14 elements. How many subsets of S have at most 4 elements

A: At most 4 means 4 or less.  Let us denote X=number of elements

Q: Show that A = {2,3,4,5} is a proper subset of B = {2,4,5,6,3}

A: A set X will be called a subset of Y, if each elements of X belongs to the set Y . A set X will be…

Q: How many proper subsets does the set T={h,f,k} have

A: A set is given by, T = h, f, k. The objective is to find the number of proper subsets the T have.

Q: Let S be the universal set, where: S={1,2,3,...,28,29,30}S={1,2,3,...,28,29,30} Let sets A and B be…

A: On solving this we will get

Q: Consider the following sets: A = {1,3,5,7,9, B, D, F), B = {0,3,6,9, C, F) and C= (0, 2, 4, 6, 8, A,…

A:

Q: Let X = {a, b, c, d, e} and let T= {X, ø, {a}, {c,d}, {a,c,d}, {b,c,d,e}}, then * (X, T) is not…

A: Option 2 is correct.

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: 2. How many 3 element subsets of the set {a, b, c, d, e, f, g, h, i} contain no vowels?

A:

Q: SUppose K,n EZ and O < Kcn. Prove +hat by (onsi nsi dering subsets of (1,... --- --- (^) - (":') + (…

A: The given problem is to prove the following identity using the basic mathematical identities.

Q: find fundamental set of soleubions cwith d real va lues for

A: Using differential equations,

Q: et UU be the universal set, where: U={a,b,c,d,e,f,g,h,i,j,k}U={a,b,c,d,e,f,g,h,i,j,k} Let sets AA,…

A:

Q: 1. Let X-(a,b,c} and T X={Ø,X,{a},{b},{a,B}}, (i) Write down all open subsets of X. (ii) Write down…

A: If (X,T_X) is a topological space. Then elements of T_X is called open sets and a set is closed if…

Q: Let S={1,2,3,...,18,19,20}S={1,2,3,...,18,19,20} be the universal set. Let sets AA and BB be…

A:

Q: Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * O (X,T) is not connected but it…

A: No information is given for topology on Y So i have solved only the middle question

Q: Let S = {1,2,3,...,18,19,20} be the universal set. Let sets A and B be subsets of S, where: Set…

A:

Q: Number theory

A:

Q: How can the union and intersection of n sets that all are subsets of the universal set U be found…

A:

Q: Let S be the universal set, where: S={1,2,3,...,23,24,25}S={1,2,3,...,23,24,25} Let sets A and B be…

A: Please see the explanation below

Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

A:

Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Consider that  the set S has 7 elements. The subsets can have 3 elements, 2 elements, 1 element, and…

Q: Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B…

A:

Q: If A is set of all vowels in alphabets.Then number of subsets of A is

A: Given: A contains all vowels  So, A = a, e, i , o , u Number of elements in A = 5

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

A: We use the definition of the size of a set to find the number of elements in the set B. The size of…

Q: Let UU be the universal set, where: U={1,2,3,...,18,19,20} Let sets A and B be subsets of U,…

A: The universal set U=1,2,3,....,18,19,20set A=2,4,7,8,10,14,16,17,18set B=10,12,14,17set…

Q: 1. Let the universal set be the set S = {0,2,4,6,8,10,12,14,16} and let A= {2,4,6,8}, B = {0,2,4,6}…

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: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

A:

Q: Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are,…

A: Given R and S are two Poset on a set X. (1) Consider R∩S. Since R and S are poset, therefore each…

Q: a) Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets…

A:

Q: 15 Assume that set S has 11 elements. How many subsets of S have at most 2 elements?

A: Solution : A set S has 11 elements We want to find subset of S have at most 2 elements

Q: Let S be the universal set, where: S= {1, 2, 3, ..., 28, 29, 30} Let sets A and B be subsets of S,…

A: Explanation of the answer is as follows

Q: 3. Show that if A and B sets then A – B = ANB (Note that: Using Venn Diagram is not accepted!)

A:

Q: Let S={1,2,3,4,5,6} How many subsets are there of cardinality 4?

A:

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

A: Given,          x,a,x,b,x,c,y,a,y,b,y,c is the Cartesian product of A×B.

Q: 1. Prove or Disprove: For all sets A and B, MUB- M+ B

A:

Q: prove that (1, 6) 13 an o pen set 13 an open çet.

A:

Q: Let A = {1, 2, 3} and B = {2,5} be two subsets of a universal set U {1, 2, 3, 4, 5). Compare (AUB)…

A:

Q: {r, e, v, o, I, u, t, i, o, n}_ _{t, o, I, o, v, e, r, u, i, n} {r, e, v, o, I, u, t, i, o, n} V {t,…

A: Here use definition of proper subset

Q: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C. If B is 4…

A: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C.

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”.