Ex: How moay eg. rel's are possible {2,3,4}? 5 on 3 4 3 4 3 R={(2,2), (3,3), (3,4), (4,5) , (4,4)} |How many eq- rel's 9.5 #44 TH3 are possible et of cardinality 4? on

Q: Define a smallest possible set of which both {1,3,5} and {0, 3,4 } are subsets.

A: The subsets given are {1, 3, 5} and {0, 3, 4}.

Q: Set A is the set of all natural numbers less than 30 that are divisible by 5.  Express the following…

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Q: Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have…

A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

Q: How to prove that the cardinality of the Cantor Set is equivalent to the cardinality of the set of…

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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: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

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Q: How many subsets of {0,1,...,10} have cardinality 1 or more?

A: Let  We have to find the number of subsets of that have cardinality 1 or more.We know thatIf A is…

Q: 2) The power Set p(x) of a setx_is epartial order velation according to the yelation clcoverage).

A: A relation R on a set S is called a partial order relation if it satisfies the following three…

Q: Prove that the interval (0, 1) has cardinality aleph-one.

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Q: Let X be the set comprising all numbers of the following two types: • Natural numbers; • Natural…

A: From (i) & (ii), we conclude that the function f is well defined.

Q: There are infinitely many different infinite cardinalities.

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Q: Let the universal set U = {x | x is a positive integer}. Also, let A = {x ∈ U | x is divisible by…

A: Given, U={x | x is a positive integer} The positive integers are  1, 2, 3, ... i.e. the natural…

Q: Use the numerals representing cardinalities in the Venn diagram shown to give the cardinality of…

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Q: If A={4,5,6}, find its power set P(A). What is the cardinality of this power set?

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Q: Are the sets A_4 and A_5 compact sets? Why yes, why not? Ay = (,2] A- [1, 2] u [ 3, +]

A: See the attachment

Q: How can the union and intersection of n sets that all are subsets of the universal set U be found…

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Q: Assume that A = {1, 2, 3, 5, 8, 7} B = {5, 3, 4} C = {2, 3, 5, 6} and that U is the universal set of…

A: It is basic set theory problem

Q: What is the cardinality of the power set of a set with 4 elements?

A: Introduction: The cardinality of a set:The cardinality of a set is the total number of unique…

Q: count the number of possible equivalence relations on a set of size n by providing a formula in…

A: We use the idea of partitioning to get the total number of equivalence relations.

Q: 4. Explain how bijection can be used to define the cardinality of an infinite set. Using that idea,…

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Q: Consider the following families of sets indexed by the set of natural numbers. Which among these is…

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Q: Show that {1, 2, 3}N, the set of all functions from the natural numbers to the set {1, 2, 3}, is…

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Q: Prove that each of the following pairs of sets have the same cardinality. (a) We have the sets X and…

A: In set theory, one important concept is that of cardinality, which is the measure of the "size" of a…

Q: How many subsets of {0, 1, ..., 8} have cardinality 6 or more?

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Q: How

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Q: Give the cardinality of M:{1st 5 multiples of 5}

A: Given, M:{1st 5 multiples of 5} Since 1st 5 multiples of 5 are 5, 10, 15, 20, 25. So,  M: {5, 10,…