Consider the set C={Ø,{Ø},{Ø,{Ø}}}. How many elements are there in the power set P(C)? *

Q: Let T be a set such that if the integer x is in T, then 2(x+1) is also in T. Let integer 2 is in T,…

A: To find the correct answer.

Q: (iv) The power set P(C) of C by listing down the elements directly.

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Q: Let A be a set with |A| = n. Using induction, prove that |P(A)| = 2^n .

A: To show that the cardinality of power set of A is 2n when given that cardinality of A is n.

Q: Consider the set T = {..., −34, −17, 0, 17, 34, ... } with the usual definition of less than (a0).…

A: Completeness property of real numbers:  Every non-empty set of real numbers that has an upper bound…

Q: Identify all possible proper subset relationships that occur among the following sets. A = {3n + 1|n…

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Q: O Show that if A is finite, then P (A) is finite.

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Q: (c) Prove that if A and B are finite sets, then A B is finite and A B| = |B|Al. (Hint: Use induction…

A: For (c), We are given that if A and B are finite sets. So, let |A| = m and |B| = n. Now, we need to…

Q: If C1, C2 are connected subsets of R, then the product C, xC, is a connected subset of R?,

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Q: Let A (k,s), t.en the power set of A is:

A: Set of all subsets of A is called power set of A.

Q: 9) Find the power set of each of these sets, where X, y are distinct elements: (a) {x, y} (b) {x, y,…

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Q: For a poset with the following Hasse diagram, consider the set {b, e, f}. The least upper bound of…

A: using the concept of upper bound least upper bound in hasse diagram...

Q: Cantor set is uncountable .A O

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Q: 9. Give a proof by contradiction to show if A and B are sets, then A N (BN A') = {}.

A: Suppose A and B are sets.

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) S° is the largest open set in M that contained in S.

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Q: E Let T = {1,2, 3}. List all subsets of T, not forgetting the empty set, Ø, and not forgetting T,…

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Q: [S,*]= [Z,+] and [S',*']=[Z,∘] where a∘b=a+b-1. Then ?(n)=n+1 is an isomorphism from [Z,+] to [Z,∘]

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Q: be an open subset in C and f

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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 of…

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

Q: Let T be a set such that if the integer x is in T, then 2(x+1) is also in T. Let integer 2 is in T,…

A: Given T is set of integers with 2 belongs to T.

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: From the list below, choose ALL sets that have g as a member. {{ø}} O (0} U{Ø} O (Ø)-{{Ø}}

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Q: 1. Show that if A is a subset of B, then the power set of A is a subset of the power set of B.

A: Hello, thanks for your question but according to our policy, I am answering the very first question.…

Q: Let P be the set of all positive factors of 90, and let / denote the 'divides' relation. Then the…

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Q: Let E be a nonempty subset of an ordered set; suppose a is a lower bound of E and B is an upper…

A: Let X be a non empty set. Let a∈X. Then a is said to be a lower bound of the set X if a≤x for all…

Q: 3. Let M and N be nonempty set such that M = N, then |M| = |N|. %3D

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Q: Let A = {a, B} be the set of alphabets and let L be the set of all palindromes over A. Write the…

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Q: For all s, Isin s≤ 1

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Q: b) Prove, by induction, that for any k > 1 and any choice of c1, ... , Ck E R and X1, ... , Xk E V,…

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Q: Use set-roster notation to indicate the elements in the following set: S= {n € Z | -3 < n< 1}

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Q: Suppose A is a set for which |A| = 12. How many 5-element subsets of A are %3D there? (the number of…

A: Here given   A is set for which |A| = 12  So here no of elements in set A = 12

Q: Let S be a 50-element subset of {1, 2, 3,...,87} and let T = {s+11 :sE S}. Prove that SnT+ Ø.

A: This is a question of Set theory, application of the Pigeon Hole Principle.

Q: 3 S how that Set M with n elements. a where n is a elem ent of ne tural numbers (ne IN. has 2…

A: Number of elements in M is n. To prove power set of M has 2n elements. We know that Power set of M…

Q: . Is the power set P(H),

A: Given,   And the powerset of H: . * and *' on are defined by . We have to justify that the…

Q: distinct arrangements are possible e

A: We have to find out the total number of arrangements.

Q: Form the power set P(A), where A= {a,B,y,6}

A: Given, A=α,β,γ,δ

Q: 5. Find the power set of each of these sets, where a and b are distinct elements. a. {a}

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Q: Let S be a set of four elements given by S = {A, B, C, D} with the following table. * A B c D A B c…

A: Consider the set S=A, B, C, D. Given table: * A B C D A B C A B B C D B A C A B C D D A B…

Q: 7. Let A= {a, b, #} and X {Ø, (Ø}}, Find the power set of A and the power set of X.

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Q: Construct a Venn diagram illustrating the sets below. U={1, 2, 3, 4, 5, 6, 7, 8, 9} W={3,5, 6, 8, 9}…

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Q: Let S be the set of all strings of 0's and 1's of length 4, and let A and B be the following subsets…

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Q: Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and Z?…

A: It is known that the ordering of the elements in a set does not matter. If the elements of both sets…

Q: State whether the given set E is bounded or unbounded and justify your answer with a proof. E = {z €…

A: We are given the set, E = { z ∈ Z : z ≡ 7 mod 9}. First, we will try to find the elements in E then…

Q: Define the sets D = In E N} n+1 Prove whether D is finite, countable, or uncountable?

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Q: let A to have0 al an must by

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Q: Let S be a set of n elements. Find the number of distinct subsets of S.

A: Given: Let S be a set of n elements.

Q: Prove that for every n E N if A is a set with n elements, then the power set of A, P(A), has 2"…

A: The set P(A) contains every possible subset of A, including the empty set and the set A itself.

Q: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} Use the roster method to list the elements in the set A. A=

A: Given: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} The roster form is given by

Q: Consider the relation = on the natural numbers 9...24. How many sets are in the partition of 9...24…

A: As we that '=' is the equivalence relation then we have a partition with the set of the natural from…