Given two sets: A = {a, b} B = {b, c, d} Construct the disjoint union of A and B.

Q: Use the Venn diagram shown to answer the question below. U A B II III V IV VI VII VIII Which regions…

A:

Q: Given A⋂B = {s, z, u} and A⋂C = {s, z, u, m, n} .Find how many elements the set A⋂ (CUB) has?

A: We know that A⋂ (CUB)= (A⋂B)U A⋂C

Q: Given two sets A and B, prove that the condition ACB is equivalent to the condition A N B = A.

A: We will solve the following.

Q: 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B)U C) \ D, An(BU C) \ D, An(BU (C\…

A: Example of such set A,B,C,D are given below

Q: If R is the universal set, find: 1. Q ∩ R 2. Z ∩ I 3. N ∩ I

A: Since R is universal set.

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: Consider the sets to answer the attached photo: A = {a, b, c, d, e, f, h, j} B = {a, b, i } C = {f,…

A:

Q: Indicate whether the following sets are equal. A={x, j, a, w}, D={x, a, b, y}

A: The given two sets are, A=x,j,a,w and D=x,a,b,y By definition, The two sets A and B are equal sets…

Q: Find the number of elements in sets A, B, and C using the given information. AnC-Ø,n (An B) = 6, n(C…

A:

Q: For two sets, X and Y , if  X ∩ Y = ∅ , then which of the following is true? Choose one answer and…

A: Given that For two sets, X and Y, X∩Y=∅ To find which of the following statement is true:

Q: The Venn diagram below shows the sets A, B,C and U. U A C Determine whether the given regions are…

A: We need to use given Venn Diagram to answer questions

Q: Given sets A and B, define their symmetric difference as AAB = (A – B)U (B – A). Use the set…

A: Symmetric difference of sets A and B are given by formulas: A△B=(A-B)∪(B-A)A△B=(A∩BC)∪B∩AC Here, AC,…

Q: Given the sets A = {5,6, 7}, B= {0, 1, 2, 3, ...}, and C {4, 5, 6}, tell which of the following…

A: Given the sets A=5, 6, 7B=0, 1, 2, 3, ...C=4, 5, 6 We shall check the correctness of statements a,…

Q: Find, if possible, the number of elements in sets A, B, and C using the given information: n (C…

A: Refer to the question. Use the venn diagram method to solve this problem.Now here n(A intersect B)…

Q: For any sets A, B, show that (A \ B)c = Ac ∪ B.

A:

Q: Consider the sets: A={a,b,c} B={b,c,d} C={a,c} D={d,c,b} For each statement below, state whether the…

A:

Q: For any sets A, B, and C; the distributive law states AU (B n C); that is a. (A U B) n (A U C) c. (A…

A: DeMogran's distributive law

Q: Using these sets, find the following: DU (EU F) D = {b, a, c, k} E = {t, a, s, k) F = (b, a, t, h).

A: Given, D=b,a,c,kE=t,a,s,kF=b,a,t,h D∪E∪F is to be determined.

Q: For sets A, B and C, prove that (A∩B) x C = (A x C)∩(B x C).

A: For sets A, B and C, prove that (A∩B) x C = (A x C)∩(B x C).

Q: Determine whether or not the following is true: for all sets A, B and C, (AUB) (C\A) = AU (B\C); If…

A:

Q: 사 Use the Venn diagram shown to the right to determine whether the given sets are equal for all sets…

A: Given below clear explanation

Q: A Partition of a set has 3 subsets: A, B, and C. If Pr[A]=.25 and Pr[B]=.45, find Pr[C].

A: The provided information is,P(A) = 0.25P(B) = 0.45According to the general law of probability, the…

Q: Consider the sets A = {x € Z*,x < 13 | x prime} B = {x € Z*, x < 13 | x even} C = {x € Z*,x < 13 |…

A: For three sets A, B, and C it can be said that, A ∪ B ∪ C implies the set of elements that belong to…

Q: If X and Y are two sets such that           n ( X ) = 17, n ( Y ) = 23 and                    n ( X…

A:

Q: The set {(a,b) : a EA and b EB} denoted by ...............

A:

Q: Find the intersection of the sets. {r, e, a, l}∩{l, e, a, r}

A: Given:A=r,e,a,lB= l,e,a,rIntersection set:The set containing all elements of A that also belong to…

Q: 5. Given sets A and B, define their symmetric difference as AAB = (A – B) U (B – A). Use the set…

A:

Q: If A and B are sets; A and B°denote the complements of the sets A and B, then the se (A – B) U (B –…

A: Given that: (A-B)U(B-A)U(A∩B)

Q: 5. Given sets A and B, define their symmetric difference as AAB = (A – B) U (B – A). Use the set…

A:

Q: b) B = {(x, y) : x² < e*+3y < 5y + 4x},

A: The objective is to find the closure of the given set.

Q: Given A={x,y},B={1,2,3,} and C={m,n}. How many ordered pairs are there for AXBXC

A: Elements of A×B are the ordered pairs of the form  A×B=x, y | x∈A, y∈B Given : A=x, y, B=1, 2, 3,…

Q: Given the following sets X= {a,b,c} Y= {a} Z= {a,d} In the universe U= {a,b,c,d,e}, what is (X’…

A: Sample Space (SS): The total number of possible outcomes of an event is called Sample Space and it…

Q: Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered…

A: Given that: n(A)=p, and n(B)=q

Q: Give an example of sets S and T where P(SUT)メP(S) U P(T)

A: Let, S={3,7} and T={4} be any set and P(SUT) be a power set of union of S and…

Q: Check the boxes in the accompanying figures to indicate which regions should be shaded to represent…

A:

Q: The Venn diagram below shows the sets A, B,C and U. U А B C Determine whether the given regions are…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Is the following set connected: V = {(x, y) € R² | 1<x² + y² <4}? Briefly justify your answer.

A: Connected set:- If any two points of a given set can be joined by a continuous polygonal arc such…

Q: For any sets A and B, show thatP ( A ∩ B ) = P ( A ) ∩ P ( B ).

A:

Q: Which regions represent set ANC?

A: Here use basic of venn diagram  Here in venn diagram  there are 3 events A , B and C

Q: For an element to be in the union of sets A and B, the element must be in set A in set B. but not…

A:

Q: Consider the Venn diagram shown below. For each of (i)–(iv), copy the diagran and shade the region…

A:

Q: Let A and B be two sets. (a) Show that (A°n B°)° = AU B and (AºU Bc)C = AN B. %3|

A:

Q: Prove that if A ~ B then P(A) ~ P(B).

A: Consider the provided question,

Q: Let A, B, C be sets. Simplify (A∪(B∩C))∪((Bc ∩Cc)∪C)c

A:

Q: Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)are in A × B, find…

A: In AxB the first element will be from A and the second element will be from B So, x,y,z are in A And…

Q: 10. Given sets A, B, and C, such tha |U = 175|, |A| = 42, |B| = 20, |C| = |ABC| = 4. Calculate:…

A: The formula of sets for the three  sets A, B, and C is: n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) -…

Q: Write the following sets by listing their elements between braces. 1. P({{a,b},{c}}) 2. P({1,2,3,4})…

A: Given

Q: Does the set span R3?

A: s=310,0-11,12-1Let v1,v2,v3 in R3 , if span(v1,v2,v3)=R3 then v1,v2,v3 are linearly independent.Rank…

Q: Given the following sets, perform the indicated set operations: U= {a, b, c, d, e, f, g. h, i, j, k}…

A:

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”.