Provide an example to show that connectedness is not a hereditary property.

Q: Determine whether the given pair of graphs are isomorphic. Exhibit an isomorphism or provide a…

A:

Q: topological space X is the intersection of all its closed neighbourhoods. A regular if and only if…

A:

Q: Write an equivalence relation of Set A = {1,2,3,4,5,6}

A: Set A={1,2,3,4,5,6}

Q: Prove that the relation of congruence is an equivalence relation.

A: A relation is said to be an equivalence relation if and only if the relation is reflexive, symmetric…

Q: Prove it. Establish the mapping 7 and IN.

A:

Q: {a,b, c, d} which is symmetric and (a) Give an transitive, but not reflexive. example of a relation…

A: a) Definition of symmetric, transitive, reflexive relation: Let, R be a relation on A. R is said to…

Q: Let A = {1,2, 3, 4}, R = {(1,1), (1,2), (1, 4), (2,1), (3,3), (4, 1), (4,4)}. Draw a diagraph and…

A:

Q: Is the relation with the directed graphs shown below an equivalence relation? 4. 6.

A: Let  A be a nonempty set. A relation ~ on the set A is an equivalence relation provided that ~ is…

Q: Prove that every well order is a linear order,

A: A set  is said to be well-ordered if it has a total order and has the property that every non-empty…

Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: Suppose X has the discrete topology. Then the infinite product X" with the product topology is also…

A: Suppose X has the discrete topology. Then the infinite product Xw with the product topology is also…

Q: {(a, b) acb, a and b are finite set of integers}

A:

Q: Show that any 2-cut relation (for > 0) of a fuzzy equivalence relation results in a crisp…

A: Let's take the fuzzy relation: R = 10.800.10.20.810.400.900.41000.10010.50.20.900.51 Fuzzy tolerance…

Q: Draw a single Venn diagram that represents the relationsh

A: Introduction: A Venn diagram could be a graphic that employs circles to depict relationships between…

Q: what is a connected dominating set ? And give examples

A: A connected dominating set of a graph G is a set D of vertices with two properties: 1) Any vertex in…

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: Arbitrary unions of closed sets are closed.

A:

Q: Show that the intersection of any collection of equivalence relations over a set A is also an…

A: We have to prove intersection of equivalence relations on a set is equivalence Let us suppose R and…

Q: 3. Determine whether the given pair of graphs is isomorphic. Exhibit an isomorphism (by showing a…

A:

Q: how to prove a map is unique?

A:

Q: Give an example of a mathematical object that satisfies the described proper- ties or explain why…

A: Determinant

Q: What is a homomorphism in simplest terms? Also provide an example.

A:

Q: Lecture 8 Review Exercise: 1) What does it mean if we say that a set S is closed under a binary…

A:

Q: Justify the following statement: the total degree (sum of all degrees of all vertices) of a finite…

A: Isomorphic Graphs Two graphs G1 and G2 are said to be isomorphic if − There exists a function ‘f’…

Q: - Is T a one to one mapping?

A:

Q: Propose a partial order on a non-empty finite set so that it has 3 maximal elements and two minimal…

A:

Q: Let K = {A, Ā, A-°, A-o-, A°, A°¯, A°-o}. Show that K is closed under the interior and closure…

A:

Q: what is the spanning fuzzy subgraph ? And give examples

A: We have to define fuzzy spanning subgraphs and give examples.

Q: graphing, prove that at least one of G and it's complement, G', is connected.  Draw G and its…

A: If G is connected then nothing have to prove.

Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Give a proof that the associative property is a structural property. (Start with two isomorphic…

A: We have to give a proof that the associative property is a structural property. Start with two…

Q: Define the term Connectedness?

A: In mathematics Connectedness is used to refer to various properties meaning, in some sense, "all one…

Q: (3) Let X be a connected, locally path connecte

A: Let X be a connected, locally path connected space and the functionπ1(X) is finite . We have to show…

Q: what ordered pair is an example of a topological space that is connected but not path-connected,why?

A: We use contradiction method.

Q: GIve a simple example of the Well Ordering Principle of Integers

A: We have to explain the Well Ordering Principle of Integers using an example.

Q: Finite topological spaces are always complete. True False

A: Finite topological spaces are always complete. So it is true statement.

Q: Show that any 1-cut relation (for 1> 0) of a fuzzy equivalence relation results in a crisp…

A: Consider the fuzzy relation: R =10.800.10.20.810.400.900.4100010010.50.20.900.51 Fuzzy tolerance…

Q: Draw a directed graph (digraph) for the relation on {1,2,3,4} {(1,1), (1,4), (2,2), (3,3), (4,1)

A: From the given relation {(1,1), (1,4), (2,2), (3,3), (4,1)} on {1,2,3,4}, draw a directed graph.…

Q: Show R³ is a banach space.

A: Banach space: A complete normed linear space is called Banach space. Given: To show:  is a Banach…

Q: 20 - Determine whether the relation with the directed graph shown is an equivalence relation ? a d

A:

Q: Find all equivalence relations on {1,2, 3}.

A: A relation R on a set A is said to be an equivalence relation if it is reflexive symmetric and…

Q: Drag the correct description of the transformation and congruence criterion into the empty box below…

A: Given,

Q: Show that every map on RP² can be colored by six colors, and that there is a map on RP² that…

A: I have given detailed proof for ablove questions firstly I have stated the lemma which we will be…

Q: 5. Can somcone cross all the bridges shown in this map cxactly once and return to the starting…

A:

Q: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…

Q: Show that the closure of a connected space is connected.

A:

Q: what is a maximal Matching ? And give examples

A:

Q: Suppose X has the discrete topology. Then the infinite product X with the product topology is also…

A: It is given that X has the discrete topology. Check whether the infinite product Xw with product…

Q: Define equivalence class and partition of a relation.

A: Define equivalence class and partition of a relation.