3- o is а) Нomonorphism. b) Isomorphism c) Automorphism d) None O b)

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A: Given that M and N are two R-modules. We have to show that HomM,N is not a group under composition.…

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Q: Proposition 1.43. A is the intersection of all closed subsets of X which con- tains A. Proof.…

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Q: 1. Prove the distributivity property of intersection over union ANBUC) = (AN B) U( ANC)

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Q: 2. Show that any subset of a countable set is countable. 3. Show that a nonempty set S is countable…

A: Hence any subset of a countable set is countable.

Q: Prove: If = ¿ (where a, b, c, and d are nonzero), b then d*

A: Given:               ab=cd  (where a,b,c  and d are non zero.)

Q: Cantor set is uncountable .A O

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Q: Prove by induction that for sets A1, A2, . .,An, n A¡ i=1

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Q: let R be for of King and acR.UThen a3-a Prove all that R is commutative

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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: 3. is in the span of the set { -1 Birini seçin: O Doğru O Yanlış

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Q: Suppose that 2 = {1,2,3,4} and C = {{1}, {2}, {3,4}}. Determine o(C), the smallest o-algebra on 2…

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Q: Prove that the set {a, b, c}* of all strings (of finite length) on {a, b, c} is count- able.

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Q: (2) (a) Show using set identities that AUBU (AOBOT) = AUBUT (b) Prove by contradiction that if A C…

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Q: Show that the o-algebra B of Borel sets contains all F,-sets.

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Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

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

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Q: The set Z of all integers is countable i.e., there exists a one-one onto map Ava between the set of…

A: Note: Z = {0, 1, -1, 2, -2, 3, -3, 4, -4, ...} And N = {1, 2, 3, 4, 5, ...}

Q: Prove that ord,(a + b) > min(ord,a, ord,b) with equality holds if ord,a ± ord,b.

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Q: 11. Which of the following is a subsemigroup of (Q,*) where a*b = ab/5? A. (Z, *) C. (Q+, *) B. (Z+,…

A: Given that Q,* is a semigroup where a*b=ab5∀a,b∈Q

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Q: 2. Show that if u is a SC

A: Given, if u is a solution of                          ∇2u+D(x, y)∂u∂x+E(x, y)∂u∂x=-F(x, y) in D with…

Q: Let 9= {[a,b]: a,bER}, then 9 is Borel algebra

A: TRUE ;

Q: Prove that if ACB, then A-B=0.

A: This question can be solved using the concept of set theory.

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Q: Let be 7= {x, 0, {a}, {cd}, {a,c,d}; {b, c, d, e}} topology on X = {9₁b, c, d, e}. Check if X is…

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Q: 3. Prove that a = b(mod7)is an equivalence relation by taking suitable examples.

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Q: If A subut of B. where B 18 a closo d subset of IR show that

A: Given: A is a subset of B, where B is closed subset of ℝp. To show: A¯⊆B.