Simplify the set expression (X∩Y’) ∪ (X∩Y)~X’ using the Laws on Sets.

Q: Direction

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Q: Provide a counterexample for the statement: For any sets A,B and C, А - (В -С) — (А - В) — С.

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Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: Let W = (-∞,∞) be the universal set and Q = [-3,7) and P = [-5,4]. In interval notation, determine…

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Q: Express the set in set-builder notation {24, 32, 40, 48,....,88}

A: Consider the given set. Rewrite the elements of sets as the multiple for 8. Given set=24, 32, 40,…

Q: Can I use symbols other than braces when writing sets using the roster method?

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Q: Define Open set ?

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Q: The set of elements that are members of set A or set B or of both sets is called the --------------…

A: The union of two sets is composed of elements of the same two sets.

Q: Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who arein school hockey team. Let Y…

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Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: Provide a counter example that infinity intersection of open set is open

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Q: What is meant by Intersection of sets?

A: Let A and B be the two sets. Then the set of all common elements of A and B is called the…

Q: Which of these sets are equal: {x, 1, z}, {z, 1, z, x}, {1, x, 1, z}, {1, z, x, 1}?

A: Given sets are x,1,z , z,1,z,x , 1,x,1,z , 1,z,x,1 find out which sets are equal

Q: What is the other name for the “rule method” in describing a set?  (A) roster (B) defining property…

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Q: Express (4, 10) as a set {x : |x – al < c} for suitable a and c.

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Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

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Q: Prove the set of rational number has the same cardinality as the set of natural numbers I will…

A: Consider the given set's. The set of natural numbers is defined as. N=1,2,3,… Now, the set of…

Q: Write out in words the description of the set. {x\x € W, x < 9} The set of ---Select--- X, such that…

A: To write out in words the description of the set.

Q: Define two sets, call them A and B, that makes the following statement true; if it is impossible to…

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Q: Explain what is an empty set. Give relevant example along with.

A: Empty set

Q: Explain what is a finite set. Give relevant example along with.

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Q: why Ua equals to empty set

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Q: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

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Q: The cartesian product of nonempty family of nonempty sets is nonempty صواب ihi

A: The cartesian product of nonempty family of nonempty sets is nonempty

Q: Classify the discontinuity of as a removable, jump or infinite?

A: This question is related to continuity and differentiability.

Q: Show that the set given in the image below is non convex. Please prove the result mathematically…

A: A set is said to be convex if for any two points in the set the line segment joining those points is…

Q: The set of elements in (- ∞, 9) or (- ∞, 12) or in both sets is________ . This represents the_______…

A: The set of elements in -∞, 9 or -∞, 12 or in both sets is________ . This represents the_______ of…

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Express (4, 10) as a set {x : |x − a| &lt; c} for suitable a and c

A: Write the given interval in inequality form as follows: 4&lt;x&lt;10

Q: Let X And Y be two distrecte spaces. Then X is homeomorphic to Y if and only if X and Y are both…

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Q: Determine if the union/intersection of two open sets is always open then determine if the…

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Q: The infinite in tersection of -pon Set is ofen set.

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Q: two example of open set in R, closed set in R, and the closure of that set

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Q: The set {......., -4, -3, -2, -1, 0, 1, 2, 3, 4, .....} is called the set of -------------.

A: Numbers are constructed by first starting with 1. Then all numbers which can be written as sum of 1s…

Q: Check whether The basis of folowing set not is or 2. 2.

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Q: What is meant by Union of sets?

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Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

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Q: Describe the set {TER²: doo (r,(0, 0)) = 1}.

A: To Describe: the set {x∈ℝ2: d∞(x,(0,0))=1}.

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A: Consider the given set A = {a, b, c}. A proper subset of a set A is a subset of A that is not equal…

Q: Prove that the smallest member of a set, if exits, is the greatest lower bound of the set. Correct…

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Q: Let U be the universal set of all the letters in the English alphabet. What is the complement of the…

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Q: Theorem 1.12. The union of countably many countable sets is countable.

A: We have to prove that the union of countably many countable sets is countable.

Q: The union of a infinite number of closed set need not be a Closed set Open Set Both open and close…

A: The union of infinite number of closed sets is

Q: Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable…

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Q: how that the union of a finite. number of bounded sets is bounded

A: A statement is given as, 'the union of a finite number of bounded sets is bounded. The objective is…

Q: {(x,a), (x,b), (x,c), (y,a), (y,b),(y,c)} is the Cartesian product AXB of two sets given as

A: Given,          x,a,x,b,x,c,y,a,y,b,y,c is the Cartesian product of A×B.

Q: Give example closed set and bounded set is compact

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Q: What is the possible number of reflexive relations on a set of 5 elements?

A: Introduction : We have give a set of 5 elements , we have asked for the number of reflexive…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.