1. Let A, B, and C be the subsets of U. Then by using laws of sets prove A-(BnC)=(A– B)U(A-C)

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: 5. Suppose that A is a set and {Bn}nɛI is an indexed family of sets. Prove that A - UB, = N(A – B„).…

A: I have given the proof using the properties of sets

Q: 4- A subset [a, b] R is compact set in: a- (R, Td), b- (R, T), c-Both (R, Tu) and (R, T₁) d- No one.…

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

Q: (1) *, Let A and B be sets prove the following. (c) A C B if and only if B° C A°.

A: Let A and B be sets.

Q: 2. Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly?

A: No, there is no set A that satisfies A={A}. Let A is an empty set, i.e.  A=  or  A=ϕ, in which…

Q: 1. Let A, B and C be the subsets of U. Then prove that (A – B) - (B - C) = A-B by using laws of sets

A: Using properties of set theory

Q: Suppose A, B and C are sets. Prove that if A ⊆ B, then A - C ⊇ B - C

A: Dear student in the question we can't prove,  Suppose A, B and C are sets. Prove that if A ⊆ B, then…

Q: Show by membership that for all sets A, B and C: A-(ANB) CA-B

A: Sets and relations

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 N = {m,y}}. List all the subsets of N. Let A = {j,g}. Is empty set a subset of A? Consider these…

A: Consider the given set  N=m , y Now, the subsets of the set N are,  , m , y , m , y Hence, there are…

Q: . Let A and B be two connected subset

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let A, B and C be the subsets of U. Then prove that (A UB) – C = (A – C) U(B – C) by using laws of…

A: I have just used the law of sets

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: Prove that for any sets A, B, C, ANB = AN C and AUB= AUC if and only if B = C. %3D Prove that for…

A:

Q: 1. Suppose A, B and C are sets. Prove that (A \ B) U (A\ C) = A\ (Bn C). [Prove this using elements…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. Prove that if A, B,C are sets such that ANBNC = 0, then (A\B)n(C\B) = AnC. Prove that for onu got

A: Recall that, set A\B means a set of elements of A that does not belong to B.

Q: Prove formally that A\ B= A\(An B), for any sets A and B.

A:

Q: 1. Suppose A, B and C are sets. Prove that (A\ B) U (A\ C) = A\(Bn C). [Prove this using elements of…

A: Here we will use the basic concept of set theory to prove RHS = LHS. A\B = A-B Based on the ven…

Q: Let C and D are be the subsets of some universal set U. Then D-C = C'nD is

A: We have to identify the statements as true or false.

Q: 2. The subset [a,b) of R is neither open nor closed. Prove it and construc an illustration.

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: Suppose A, B, C are sets. what do you need to show to prove the fllwing definition of subset:…

A: If x is a general element in P ,the given statement implies that each element in P is also in Q…

Q: Let C, D be subsets of a set U. By proving two inclusions, show that (Cºn D) U (C N D) = D where CC…

A: Identities of the sets

Q: If a finite set A equals the union of k subsets A1, A2,..., Ak, then the number of elements in A…

A:

Q: 1.         Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i }, C = {f, h} and U =…

A: From the given information, the given sets are:

Q: Prove that if A is a set then so is {A}!

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: 1. Prove that, if A, B, and C are sets and if ACB and ACC, then ACBOC.

A: To prove: A⊆B∩C

Q: shows that there is no topology in X based on the family B = {{a, b}. {a, b, d}, {b, d, c}}

A:

Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

A:

Q: Let A = {a,b,c,d} be the set containing the four elements a, b, c and d. Let S = {X |X is a subset…

A: Sets

Q: 1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a…

A: This question is related to Set theory, We will solve it using given information.

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

A:

Q: Is {1} proper subset of A  A={x,{y},1,2,3,{2,3},{3}}

A: A proper subset of a set A is a subset of A that is not equal to A.Or in other words, if B is a…

Q: Suppose A, B, and C are sets. Prove that (AU B) – C C AU (B – C). - -

A:

Q: Show by membership that for all sets A, B and C A - (AnB) CA-B

A:

Q: Set C and the universal set U are defined as follows. U={p,q,r,x,y,z} C={p,q,x}

A: Given,        Set C and the iniversal set U are defined as follows :         U=p,q,r,x,y,z…

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: 1. Suppose A, B, and C are sets, A. Prove that: AX (Bn C) = (A X B) n (A x C) %3D

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Let A, B and C be the subsets of U. Then prove that (A UB) -C = (A – C)U(B – C) by using laws of…

A: 1) It is the question of computer science.

Q: 5. If X any Y are sets, then X-Y {r€X: z4Y} If X is open set and Y is closed set. Prove that (a) X-Y…

A: Let X is open set and Y is closed set

Q: The sets A and B have 6 and 9 elements respectively, such that A is proper subset B , then the total…

A: Given that set A and set B have 6 and 9 respectively. Now that A is a proper subset of B which means…

Q: 1. Prove the following statements about sets A and B. A B= AN Bº %3D

A: Given: Let A and B be two sets. To prove,A-B=A∩Bc

Q: 1. Are the two sets (An B)UC and A - (Bn C) the same set? Use Venn Diagram shadings to prove your…

A: As per our Bartleby guidelines, we are allowed to answer one question per query, Please ask Q2 as a…

Q: 2. If A, B and C are sets, use a membership table to prove or disprove: A U (B N c) = (A U B) n (A U…

A: First we prove that left hand side is subset of right hand side and then right hand side is subset…

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: 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: Let X = {a, b, c, d,e} and let T= { X, Ø, {a}, {a,d}, {a,e} }, then * O (X,T) is Hausdorff and…

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”.