{a,b,c,d), T₁ = {0, x, (a), (b}, {a,b}, {a,c}, {a,b,c}} {a}, T1 Let X = and T2 {0, X, {a}, {c}, {a,b}, {a,c}, {a,b,c}} be topologies on X. Let F₁ and F2 be the set of all closed sets associated with T₁ and T2 respectively. (a) Write down all the elements for the sets Fi and F2. (b) Find the following and justify whether each of them is a topology or not: i. T1 U T2. ii. T₁ T2. (c) Is there any relationship between either F₁ UF2 or F₁ F2 and the topology identified in 2(b) above?

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Let A= {1,2,x,y,z}, and B= {1,2,3,z}. How many distinct elements are in (A*B) intersect (B*A

A: Given that A=1,2,x,y,zB=1,2,3,z To find the number of distinct elements in A×B∩B×A:

Q: 3. Describe span S if: a) S= {(1,1); (2 ,6); (7,12)} b) S= {(1,0,2); (3,2, –7); (–1,–2,11)} c) S=…

A:

Q: Let f:XT, → XT, such that f({a}) = {b, c} į Is fa continuous function? i yes,no, or can't you tell?…

A: Let (X, ΤX) and (Y, ΤY)be topological spaces A function f : (X, ΤX) → (Y, ΤY) is continuous  if…

Q: Let U​ =​{1, 2, 3, 4, a, b, c, d, e​}, E​ =​{1, 3, 4, c, d, e​},F​ =​{1, 2, b, c​}, and G​ =​{1, 2,…

A:

Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

A:

Q: Let X={a,b,c,d), f = ((a,b),(b,a),(c,c),(d,d)}CX×X, and g= ((a,d),(b,a),(c,b),(d,c)}CX×X. Find gof.…

A: Use the definition of composition of functions to solve this problem as in next step.

Q: In (Z24, €) find the orders of the elements 3, 4, 6, 7, and 18.

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Let C denote the set of all ordered pairs (a, b) with a,b & R. L.e., C:= {(a,b): a,b € R}. Define…

A: NOTE: According to guideline answer of first three related subpart can be given, for other please…

Q: 3. Which of the following statements are true? There may be more than one correct answer. A. Ø CA B.…

A:

Q: Let X = (1, 2, 3, 4, 5, 6) and let T1= (X, 4, {3}, (1,2,3), (2,3,4), {2}} and T2 = {X, 4, (2),…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let W = (0, 1, 3}, X = {1, 3, 5), Y = (3, 4} and Z = {(1, 2), (3, 4), (1, 3),(2, 4). Compute (X x Y)…

A: The given problem is to find the Cartesian product of given sets and verify the Cartesian product…

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: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

A:

Q: 6. For A, B, subsets of R, define A+B= {a+b : a € A,b € B} and A·B = {ab : a € A, b E B} (a) For A =…

A: Answer: As per guidelines we can do only 3 subparts of question and the solution of this is given…

Q: Suppose f : B C where B = {a, b, c}, C = {2, 8, 10}, and f is defined by f = {(a, 8), (b, 10), (c,…

A:

Q: Let A, B, C be subsets of X. show that Av (Bnc) - (AUB)n (AUC) AnCBUC) = (ANB)~ (ANC)

A:

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} %D are two sets. find R = {(x, y): x EX and * y EY and…

A:

Q: Let R1 = { (a,-1), (c,0), (d,1) } and R2 = { (a,-1), (c,-1), (d,0), (u,0), (u,1)} be subsets of A *…

A:

Q: Let A = {0, 1, 2} and let B = {-2, 0, 1, 2}. %3D

A: Given,        A=0, 1, 2, and B=-2, 0, 1, 2

Q: Write out the elements of the set 2X where X= = {1,{0}, Ø, {2,3}}.

A: