spac (a- Open and not closed, b- closed and not open, c- open and closed, d- Not open and not closed. 3- If X = {a, b, c, d, e} and T = {0, X, {a}, {c, d}, {a, c, d}, {b, c, d, e}} is topology on X, then the components of X are: a- {a} and {c, d), b- {a} and {a, c, d), c- {a} and {b, c, d, e}, d- X.

Q: Let A, B be set with A non-empty. (a) Prove that if A C B, then A, B are not disjoint. (b) What if…

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Q: (a) Define relations S and R on the set A = {a,b, c, d} as follows: S = {(a, b), (b, c), (c, d), (b,…

A: Given problem is :

Q: I. Let U = {-2, -1,0, 1, 2, ..., 10}, A = {a € U : a is even}, B = {b e U : b is odd}, C = {c € U:c…

A: As per the instructions we will be solving only the first three subparts. Let U = { -2, -1, 0, 1, 2,…

Q: Suppose X and Y are subsets of some universal set. De Morgan's laws provide expressions for the…

A: X∪Yc=Xc∩Yc

Q: the collection of all close subsets of R is called the topology of R

A: To check: Whether the statement is true or false: Given: The statement is "The collection of all…

Q: Consider the sets A = {1, 2, 3, 4} and B = {a, b, c, d}, and the relations σ = {(1, b), (2, c), (3,…

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Q: Exercise 1. Let X = {a, b, c, d, e}. Which of the following families is a topology? Why or why not?…

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Q: Let A and B be distinct elements in T. Show that An BET. Case 1: A and B = R AnB =Øn R=Ø E T by a.…

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Q: Let Asfl,2,3} and The relations Ri=f(),(2,),(3,2) | find the following Ye lations

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Q: Q. Let X = {a,b,c,d}, T = {o, X, {a}, {b,c,d}}. Then the topological space (X,T) is a. Normal and…

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Q: Let X = {a, b, c, d, e} and7 = {X,6. {a}. {c, d}, {a, c, d}, {b, c, d, e}} be a topology on X, then…

A: Details solution given below.

Q: Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c),…

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Q: This question refers to unions and intersections of relations. Since relations are subsets of…

A: The objective of this question is to find the Cartesian product of sets A and B, and the relations R…

Q: Let T={X, {a}, {a,b).{a,c,d}, {a,b,c,d}, {a,b,c}} be a topology on X=(a,b,c,d,e). (ii) Find N.…

A: Given : (X, T) be a topological space,  where  X = {a, b, c, d, e} and T = {X, ϕ, {a}, {a, b}, {a,…

Q: Let the universe of elements include these letters: p, q, r, s, t, u, v, w, x, y. The first set A…

A: The universe set contains the elements: p, q, r, s, t, u, v, w, x, y The set A contains the…

Q: Say whether (?, ?) is a topological space. Briefly explain your answer i. ? = R, and ? =…

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Q: Is T ={∅, X, {1, a}, {1, b}, {2, c}, {1, a, b}, {1}} a topology on X = {1, 2, a, b, c}? Why?

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Q: Q1.Consider X ={a,b, c, d, f, g} .Let T={ó, X, {a,b, c} ,{g};{a,b, c, g}} (a) Prove that T is a…

A: Since you post a question with multy part, we solve only first three, if you need any particular…

Q: if

A: R is not connected if T is the finite closed topology.

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

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Q: Given the universal set U = {a,b. A = {t, r,i,a,n,g,l, e, s}, B = Find: • (AU(BOC)) ● ((Aºn B) nC)…

A: According to the Bartleby guidelines experts solve only one question and a maximum of three sub…

Q: 2. Let X = {1,2, 3, 4} and let T = {ó, X, {1}, {3}, {1,3}} be a topology on X, then {2,4} is %3D a.…

A: Given X = 1 , 2 , 3 , 4 and T = ∅ , X , {1} , {3} , {1 , 3} is a topology on X Then open sets of (X…

Q: Consider X = {1, 2, 3, 4, 5} where the topology is {UC X|1 € U}. Determine whether or not X is…

A: Connected Space: A space can be separated if it can be broken up into two disjoint open sets. Let X…

Q: 1. Let A, B, and C be sets such that An Bn C + Ø. Draw a Venn diagram for each of the following set…

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Q: Cardinality: Let A and B be sets. We write A B (and say A has the same cardinality as B) if there is…

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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: Let U= {1,2,3,4,5,6,7,8,9,10,11} A= {3,5,8,11} B= {2,5,6,7,8} C= {3,4,6,7,8,10,11} D= {1,3,5,6}…

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