Given sets A and B, how many constant maps are there from A into B? Give an example.

Q: Define the sets A, B, C, D, and E as follows: A = {x € R: x 2} C = {x € R: |x| < 2} D = {x € R: |x|…

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Q: For each set partition P of each set X, describe the induced equivalence relation (a) X = {a, b, c,…

A: Given, For each set partition P of each set X, describe the induced equivalence relation ~p on X.

Q: Let R = - b ,be Z}and let ø : R→Z be a mapping defined by : b = a-b. a a

A: We will find out the required value.

Q: given two sets X-{-1,0,1} and Y={u,v,x,y,z}. There are mappings from X to Y.…

A: The set X=-1,0,1 and Y=u,v,x,y,z

Q: The set G = :a is closed under addition %3D 0 2a

A: Use the closure property of addition.

Q: Let CI(A) means the closure of A.. If A = [0, 1), Bd(A) = {5}, then Cl (A)

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Q: For any topological space (X, T) and A C X, the set A is closed. That is, for any set A in a…

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

Q: given two sets X={-1,0,1} and Y={u,v,x,y,z}. There are 125 mappings from X to true or false

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Q: Let X, Y be two sets. Prove that X × Y C P(P(X U Y )).

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Q: A map f:x-y is said to be an open map if for every open set U of X, the set f(u) is open in Y. Show…

A: Given, a map f: X→Y is said to be an open map if for every open set U of X, the set f(U) is open in…

Q: Let X, Y be two sets. Prove that X × YC P(P(X U Y )).

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Q: We defined the relation between sets by A ~ B means that there there is a 1-1 correspondence ƒ : A →…

A: We define the relation ~ between sets by A~B means that there is a one-one correspondence f:A→B Show…

Q: 1. Find the sets of interior points and boundary points of each set and classify the set as open,…

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Q: For sets A, B ⊆ R, let A + B = {a + b | a ∈ A, b ∈ B}. For closed sets A, B ⊆ R, A + B is not…

A: Point wise summation of two closed set may not be closed.

Q: You are given two sets, A = {a,b,c,d} and B = {1,2,3}. How many relations can be defined from set A…

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Q: On sets, the relation x R y given by there exists a bijective function from the set x to the set y'…

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Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: Given sets A and B, how many constant maps are there from A into B?

A: Given Set A and B Let |A| = m |B| =n

Q: Let C and D be finite sets and let f: C D and g: D C be two functions such that Vy eD f(g(y)) = y…

A: If there exists an one-one map from D to C then "|D| &lt; |C|" or "|C| &gt;|D|".

Q: The continuous image of a connected set is connected. That is, if X is connected and f : X–→ Y is…

A: We prove this via contradiction. We assume that f(X) is not connected then X is not connected. And…

Q: f is said to be a if it is both one to one and onto. That is, there is a one to one correspondence…

A: f if said to be a------- if it is both one to one and onto.

Q: If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an equivalence…

A: Given, R1 and R2 are equivalence relations in a set A. So, both R1 and R2 are Reflexive, Symmetric…

Q: For sets A and B, define A+ B = {a +b: a € A, b e B}. (a) Prove that if A and B are open, then A+ B…

A: Given : A and B are two sets and a set A+B is defined as, A+B=a+b:a∈A,b∈B

Q: Here are the arrow diagrams of two maps f and g: в a And here are two possible results for the…

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Q: If H is a subgraph of G, then show that dg(u,v) <dí(u,v).

A: A graph G illustrates how the vertices and edges are connected. Thus a graph is an ordered pair…

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c), (b,d),(b,e),(d,

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Q: Let S and T be finite sets, and let f: S T be a map. Then |S| = IS {}| YET Select one: O True OFalse

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Q: . Show that every map f : A → B of sets decomposes as hog where g : A → C is surjective and h : C →…

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Q: Let S = {1,2,3,... 18} and define the relation R by xRy if xly. Draw the Hasse diagram for R.

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Q: If Ps is a partition of (a, 6], find a

A: Given interval is, a,6 The formula for the partition is, ∆x=b-an

Q: Let X be a nonempty set and fix x E X. Define (1, rE A (A) = 10, 4 A

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Q: If n&lt;m then every linear map T: IRn -&gt; IRm is one-to-one. Is this statement true or false?

A: The given statement is

Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

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Q: 4) Let X be a finite set and f : X → X a map.

A: Given, X be a finite set and f : X→X  a map.

Q: d b

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Q: Choose the mapping diagram of this set of ordered pairs: {(6, 12), (12, 24), (18, 36), (24, 48),…

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Q: Find all maps ¢:(Z,+) → (Q*, ×) satisfying O (a + b) = ¢(a) × ¢(b) Va, b e Z

A: We derive the function from the given properties.

Q: Sets F and G are defined as follows. F={e,f, g} G=(a, b, e)

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Q: For (a, b),(c,d) EN×N define the relation (a, b) ~ (b,c) if and only if ab = cd. Is this relation…

A: Explanation of the answer is as follows

Q: Determine if the set S is span set of %3D R2x2. Solution:

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Q: Given an ordered pair (a, b) E R x R with a 0. Define the mapping a,b) : R → R by (a.b) (2) = az + b…

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Q: Is the set θ={((x,y),(3y,2x,x+y)) : x,y∈R} a function? If so, what is its domain and range? What can…

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Q: If A and B be measurable sets, ACn BC is measurable.

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Q: Recall that given f : A → B and subsets X C A respectively Y C B we can define the direct image f(X)…

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Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c),(b,d),(b,e),(d,e)}

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Q: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →…

A: The complete solutions is in given below