Let A = {distinct letters occurring in the word HIPPOPOTAMUS}. What is |A|, the cardinality of the set A ?

Q: Do the sets [0, 1] and [0, 1/2) ∪ (1/2, 1] have the same cardinality? Either give an explicit…

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Q: Let A be a set and let B be a proper subset of A. Is it possible for B to have the same cardinality…

A: Given: Let A be a set.And B be a proper subset of A.

Q: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: For each given set, determine if the set is finite or infinite. If finite, give the cardinality. Set…

A: A set which contains finite number of elements is called a finite set.  A set which contains…

Q: 14. Assume that R is a well-founded relation, x is a regular infinite cardinal, and card{x | xRy} <x…

A: Given That :  R is a well-founded relation, k is a regular infinite  cardinal, card{ x|xRy}&lt;k…

Q: What is an example of two equivalent sets with the same cardinality BUT DO NOT HAVE a one-to-one…

A: Take A as, 1,2,3 and B as 3,4,5 The cardinality of A and B is 3. Now let's define a function.

Q: Suppose S is a set with cardinality n. What is the cardinality of the power set of S ? Are there any…

A: Suppose S is a set with cardinality n. Then power set of S contains 2n elements . Power set of any…

Q: Prove that if A and B are transitive sets, then A ∪ B and A ∩ B are transitive sets

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Q: Let A be the set of even positive integers less than 40 and divisible by 4. What is the cardinality?

A: This is the question from set theory.

Q: Prove that the set of irrational numbers has the cardinality of R.

A: In informal terms, the cardinality of a set is the number of elements in that set. If one wishes to…

Q: 4. Any non-empty set A and its power set P(A) do not have the same cardinality (i.e. there exists no…

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Q: Set A is a subset of Set B.  Set B is a subset of Set A.  Thus, Set A and Set B are equal and have…

A: follow next step

Q: 2. Show that Z has the same cardinality as the set O of odd integers.

A: Given below the detailed solution

Q: "A proper subset of a set A is a subset of A that is not equal to A". According to this definition,…

A: We are given a definition of proper subsets: " A proper subset of a set A is subset of A that is not…

Q: Let X be finite set with cardinality=n. Prove that the power set P(X) has cardinality 2^n

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Q: Let A be the set of letters of the alphabet between g and m. Express A in roster form and then in…

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Q: = U.

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Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

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Q: Consider the non empty sets A and B such that A and B have the same cardinality. Prove, for any set…

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Q: Prove that if A is transitive set, then A+ is also a transitive set.

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Q: Let A and B be sets. Show that A∪(A∩B) =A using a traditional verbal proof, a series of equalities…

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Q: Let X be a set and P(X) its power set. Explain what it means that the cardinality of P(X) is…

A: It is required to explain the meaning and to prove that the cardinality of power set P(x), of X, is…

Q: Let U be universal set of all the students of Class X of a coeducational school and A be the set of…

A: In a coeducational school, there can be only boys and girls in school. Since, A is the set of all…

Q: Elements that are in the universal set but not in the set A, are members of the set called, of A.…

A: Universal set : Any set that contains all the sets is called Universal set Subset:  All the elements…

Q: For each n ≥ 3, find the number of subsets of {1, 2, . . . , n} of cardinality greater than 2 with…

A: Let X=1,2,3,....n The number of subsets of X with m elements is given by, Cmn

Q: Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set.

A: we have to prove that AUB is infinite set.  Since, given A is infinite set. since we know that…

Q: 4. Prove that the cardinality of the natural numbers is strictly less that the cardinality of the…

A: "According to Bartleby  guideline, Handwritten solutions are not provided" To prove that the…

Q: Indicate the cardinality of the set A, defined as the union of four sets of cardinalities 22, 31,…

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Q: Let U be the universal set consisting of all positive even numbers. Let A be the subset of U…

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Q: Show that the setA={1/5,1/9,1/13,1/17, ...} has cardinal number א0 by establishing a one-to-one…

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Q: Use counting to determine the whole number that corresponds to the cardinality of these sets. (a) C…

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Q: Show that the following pair of sets have the same cardinality. A = (5, 9] and B = (1, 2) ∪[4, 7]

A: Two sets A and B have the same cardinality provided there is a bijection from A to B.

Q: Show that the given set has a cardinality of No by establishing a one-to-one correspondence between…

A: Here the function is  f(n) = -6n-6  Consider two points n1, n2,  f(n1) = f(n2) should imply n1 = n2

Q: (6) A subset A of R is called co-finite if its complement R\ A is finite. What is the cardinality of…

A: Given a co-finite topological space of reals. We have to find the cardinality of co-finite sets.

Q: An infinite cardinal number a is said to be dominant if it satisfies the following condition: if b…

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Q: 19. What is the cardinality of each of these sets? b) {{a}} d) {a, {a}, {a, {a}}} a) {a} c) {a, {a}}

A: Given the set a). {a} b). {{a}} c). {a,{a}} d). {a,{a},{a,{a},{a,{a}}} We find the cardinality of…

Q: Determine the cardinality of each of the given sets: a) The set T of counting numbers that are…

A: The pair of sets are equivalent if there exists a bijection between then. We product the example of…

Q: Prove that if A is a set then so is {A} but do NOT use an argument that involves stages explicitly.

A: 3 Given A is any set. We have to prove that A is also a set. Since, A is any set Then as every set…

Q: If a set B has 64 proper subsets of odd cardinality, what is |B|? *

A: Total no os subsets of any set A, with cadinality 'n' is- 2^n Now the no of proper subsets of of A,…

Q: 3. Prove that if A is a set then so is {A} but do NOT use an argument that involves stages…

A: Let A is any set then as every set is a subset of itself then, A⊆A⇒A∈PA⇒A∈PPA

Q: Do the sets [0,1] and [0,1/2)∪(1/2,1] have the same cardinality? Either give an explicit bijection…

A: Yes, the sets 0,1 and 0,12∪12,1 have the same cardinality.

Q: Let A = {a, b, c, d) and B = {x,y}. Use the set-roster notation to write each of the following sets.…

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Q: Show that if A and B are finite sets, then A ∪ B is a finite set.

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Q: Let A1,A2,.......,An be countable sets. Prove that  A1 x A2 x.............An = { a1, a2,…

A: Let A1,A2,.......,An be countable sets. Then we have to show that    A1 x A2 x.............An = {…

Q: cardinality

A: The set of real number and set of complex have the same cardinality. But there is not one to one…

Q: The cardinality of a finite set A, denoted by Al, can provide the of A as equal to 21A

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Q: Let A and B be subsets of a universal set U, show that ACBif and only if BCA.

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Q: Show that Z has the same cardinality as the set E of even integers.

A: In order to prove that ℤ and set of even integers E have the same cardinality. (i.e) we need to find…

Q: Prove that if A is a transitive set then UA is a transitive set.

A: If A is a transitive set then, It is proved that ∪A is a transitive set as shown below.