If X and Y are two sets, then X∩(Y∩X)c equals a. Ø b. Y c. X d. X∩Yc

Q: Let A, B, C be three non-empty sets. Suppose that A× C = B× C. Prove that A = B

A: Here given that A, B, C be three non-empty sets. And suppose that A×C=B×C. We have to prove that…

Q: Which of the following pairs of sets are equal? Justify your answer.(i) X, the set of letters in…

A: i) X, the set of letters in “ALLOY”. So, X={A,L,O,Y} B, the set of letters in “LOYAL”. so,…

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

A:

Q: Consider A = {x,y,z} and B = {w,x, y}. If U = AUB, Wwhich set is equal to (B\A)'? %3D Note: B\A =…

A: Given the sets  A={x,y,z}B={w,x,y} U=A∪B therefore  U=x,y,z,w Now B-A=w    (All the elements of B…

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

A: Since R is universal set.

Q: Let R = {a}, S = {x, y}, and T = {p, q, r}. Find each of the following sets.a. R X (S X T)b. (R X S)…

A: Cartesian product of set A and B is defined as:

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: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

Q: Consider A = {x, y,z) and B {w, x, y}. If U = AUB, which set is equal to (B\A)'? Note: B\A = B- A.…

A:

Q: (4.2) For sets A, B and C, prove that (An B) x C = (A x C) n(B x C).

A: Here we have to prove that (A∩B)×C=(A×C)∩(B×C)

Q: Which of the following statements is true about the three sets A.B.C defined below: A=[ – 4,4]…

A: The given three sets are: A=[-4,4]B=[-6,2]C=[-2,6] i.e. the set A consists of the elements…

Q: Let the domain of x and y be all countries. Let W(x): "x is in the west", E(y): “y is in the east",…

A:

Q: If either A or B empty set then Ax B equal empty O A

A: The solution is given as

Q: Consider A = (x, y,z) and B = (w,x, y). If U = A U B, which set is equal to (B\A)'? Note: B\A = B-…

A: The union of set A and B is denoted by A∪B has elements both inset A and B The complement of A has…

Q: Establish formally, whether the following set is open, closed, or neither closed nor open (justify…

A: We will use the basic knowledge of set theory and point-set topology to answer this question…

Q: Let U = {x | x is a letter in the word %3D GUADALARAJA}, where this is the universe set. Also, let M…

A:

Q: If sup A < inf B for sets A and B, then there exists a c€R satisfying a <c<b for all a EA and bEB.

A:

Q: If A and B are sets; Aºand Bºdenote the complements of the sets A and B, then the set (A – B) U (B –…

A: Given:- If A and B are sets; Ac and Bc denote the complements of the sets A and B, then the set (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: Suppose that A, B, and C are sets such that A ⊕ C = B ⊕ C. Must it be the case that A = B?

A:

Q: Consider whether the following statements are true or false: a. The intersection of any two convex…

A: To state true or false

Q: Let A and B be sets. Then B (B – A) is equal to the above A N B

A: The Venn diagram for 2 sets can be drawn as follows.

Q: Select the law that establishes that the two sets below are equal: Gn (GU Z) = G OAbsorption Law O…

A: Sets identities

Q: What can you say about the sets A and B if we know that a) A ∪ B = A? b) A ∩ B = A? c) A − B = A? d)…

A: (Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Does the set S = {(1,2, 3), (0, 1, 2), (-2,0, 1)}span R³? %3D O Yes O No

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

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: Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C Ax (BUC) = (A x B) U (A x C),…

A: SOLUTION-

Q: 1. Decide whether the folloring stabe ments ae false . Justify true or (a) YxeTR, ¥yeR, x²-y² z xy…

A: 1. a ∀ x ∈  R, ∀ x ∈  R, x2+y2 ≥ 2xy  TRUE. Because,  ∀ x ∈  R, and ∀ x ∈  R we have (x-y)2 ≥ 0.…

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: Suppose that (x, y) E (A \ B) × C, for sets A, B,C C S. Then a E A and r¢ B, and y E C. This implies…

A: Use the following definitions, to prove the given result. Let A and B be two sets. The Cartesian…

Q: Let A, B and C be non-empty sets and let X= (A-B)-C and Y=(A-C)-(B-C) .Check whether X=Y or not.

A:

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

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

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: The intersection of sets A and B is denoted by which of the following?(a) A ∩ B (b) A ∪ B (c) A ⊆ B…

A: Sets are represented as the collection of different objects . There can be a finite set or an…

Q: determine which of the following sets are equivalent to the set (x,y,z) a. (w,x,y,z) b. (1,5,17)…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

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: Consider A = {x,y,z} and B = {w,x, y}. If U = A U B, which set is equal to (B\A)'? Note: B\A = B –…

A:

Q: Are the sets Z x Z; ((x.y): x*y?) closed in (R , | |) ? What about the sets (0,1]U(2,3); [0, 00) in

A:

Q: If A and B are two sets satisfying A∖B=B∖A what can we conclude about A and B? Explain.

A:

Q: Let A, B and C be any sets. Which of the following is equal to (A U C) n (B \ C)? Select one: a. (A…

A: Solution is given below:

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: d) Let X, Y, Z be sets. Calculate |X UYU Z| if |X| = 50, |Y| = 90, |Z| = 71, |X n Y| = 8, |Xn Z| =…

A: Given that X, Y and Z be the three sets.

Q: What is the size of the symmetric difference of two finite sets A and B, that is AA BI ? o IIAI -…

A:

Q: The Cartesian product of finite and nonempty sets can be illustrated by the intersections of a…

A: Given:  a=nA and b=nB To find: Explain why the number of intersection points in the crossing line…

Q: Consider A {x,y, z) and B= {w,x,y}. If U AUB. Which set is equal to (B\AY? Note: B\A = B-A. {w}…

A: Use set properties