Set builder notation example
[PDF File] Cheat Sheet of Mathemtical Notation and Terminology
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Cheat Sheet of Mathemtical Notation and Terminology Logic and Sets Notation Terminology Explanation and Examples a:=b defined by The objectaon the side of the colon is defined byb. Examples:x:= 5means thatxis defined to be5, orf.x/ :=x2 *1means that the functionf is defined to bex2 * 1, orA:= ^1;5;7‘means that the setAis defined to …
[PDF File] CXC CSEC MATHEMATICS Lesson UNIT Three: Set Theory
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Example: A possible description of the set P = {2, 3, 5, 7, 11, 13, 17} is P is the set of prime numbers less than eighteen. You must also be able to list members of a set given a description of the set. (Ex 1a page 3). ... You may use set builder notation to describe a set. Consider the following notation:
[PDF File] Basic Information About Sets and Interval Notation - Furman …
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is read as \G is the set of all x, such that x is a person ::: London Olympics." Notice how in this set-builder notation the colon (\:") is read \such that." Some people use a vertical bar (\j") instead of a colon in set-builder notation. Practice 1. Write set-builder notation for the sets S and B de ned above. Practice 2.
[PDF File] CHAPTER 2
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Example: Converting from Set-Builder to Roster Notation. Express set . A = {x | x. is a month that begins with the letter M} using the roster method. Solution. There are two months, namely March and May. Thus, A = { March, May}.
[PDF File] Set notation and concepts
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A.2 Set-builder notation We will often build a new set by selecting elements from other sets and doing operations on these elements. We use the very flexible set-builder notation for this. A set builder has the form fe jpg, where e is an expression and p is a list of predicates separated by commas. Typically, p will contain predicates of the form
[PDF File] Interval Notation - Ohio State University
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more) intervals together to make a single set. Example: ( −9, −3 ) ∪ [ 2, 5 ) This means that you have the interval ( −9, −3 ) and the interval [ 2, 5 ) .
[PDF File] CS 220: Discrete Structures and their Applications
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Set Operations. A Ç B = { x : x Î A and x Î B}. Example: {1,2,3} Ç {1,3,5} = {1, 3} Two sets are called disjoint if their intersection is the empty set. The union of sets A and B is the set that contains those elements that are either in A or in B, or in both. È B = { x : x Î A or x Î B }.
[PDF File] 2. Sets (Part I)
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Extensions: A = fx 2SjP(x)gis the set of all elements x in S such that the open sentence P(x) is a true statement. A = fTjP(x)g, where T is an expression involving x and P(x) is an open sentence. EXAMPLE 1. Use set-builder notation and its extensions to describe the following sets in two di erent ways: a) O b) E c) N d) Q e) 5Z EXAMPLE 2.
[PDF File] Set Notation & Interval Notation - Vancouver Community College
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notation and set notation. SET NOTATION Set notation is useful especially when we have a small, finite number of solutions, rather than a range of solutions. Take the equation x² = 9. There are two answers: 3 and −3. The list of all possible solutions to a problem is called its solution set and we should write it as a set using roster ...
[PDF File] 1 Sets and Set Notation. - NDSU - North Dakota State University
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student should easily verify that Y = [5;10) from Example 1 (3). In general, given a set Aand a precise mathematical sentence P(x) about a variable x, the set-builder notation should be read as follows. f x2A : P(x)g \The set of all elements xin A such that sentence P(x) is true for the element x.
[PDF File] DISCRETE MATH: LECTURE 1 - Saint Louis University
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Another way to specify a set is called the Set-Builder Notation. Let S denote a set and let P(x) be a property that elements of S may or may not satisfy. We may de ne a new set to be the set of all elements x in S such that P(x) is true. We denote this set as: fx 2SjP(x)g For example: E = fn 2Rjn is a positive even integerg= f2;4;6;8;:::g ...
[PDF File] MATH 301 INTRODUCTION TO PROOFS - - sets - functions
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An alternate form of set-builder notation uses an expression involving one or more variables to the left of the vertical bar, and the range of the variable(s) to the right. The elements of the set are then the values of the expression as the variable(s) vary: {expr(x) |x ∈X}is defined to mean{y |∃x ∈X, y = expr(x)} Example The expression ...
[PDF File] 1.3 Sets and Set Notation
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NOTATION set-builder notation Even more important for large (usually in nite) sets is the following set-builder notation: Let Udenote a universal set. The notation fx2Ujsome property that xis to satisfyg is extremely useful in many cases where roster notation fails. Here, the vertical bar ‘ j’ is read as such that or with the property that.
[PDF File] Chapter 5 Sets - University of Illinois Urbana-Champaign
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Set builder notation has two parts separated with a vertical bar or a colon. The first part names a variable (in this case x) that ranges over all objects in the set. The second part gives one or more constraints that these objects must satisfy, e.g. 3 ≤ x ≤ 7. The type of the variable (integer in our example) can be specified either ...
[PDF File] Chapter 3 Set Theory - University of Victoria
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The elements of a set described using set-builder notation are those objects of the given type that make the stated condition true. For example, the elements of the set fa=b: aand bare integers; and a=b= 0:25gare exactly the fractions whose numerical value is 0.25. There are in nitely many of these including 1=4;3=12 and 5=( 20).
[PDF File] Vector Spaces - University of Pennsylvania
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Set notation Subspaces Di erential equation example Show that the set of all solutions to the di erential equation y00+a 1(x)y0+a 2(x)y = 0 on an interval I is a subspace of C2(I). The set of solutions to a homogeneous linear di erential equation is called the solution space.
[PDF File] Sets and set operations - University of Pittsburgh
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Definition: Let A and B be sets. The difference of A and B, denoted by A - B, is the set containing those elements that are in. but not in B. The difference of A and B is also called the complement of B with respect to A. Alternate: A - B = { x | x A x B }. Example: A= {1,2,3,5,7} B = {1,5,6,8}
[PDF File] CS 332: Theory of Computation Prof. Mark Bun Boston University February ...
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3 = the set of all strings over alphabet fa;b;cgthat have length at least 3 and have b as their third symbol. (b) L 4 = the set of all strings over alphabet f0;1gthat either start with 0 and have odd length, or start with 1 and have even length. 3.Which of the following statements are true or false, for all alphabets ? For each, provide either a
[PDF File] 1.1 Interval Notation and Set Notation - Big Ideas Learning
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Write the set of numbers in set-builder notation. 6. (−∞, −1] or (1, ∞) 7. the set of all integers except −4 Using Set-Builder Notation Another way to represent intervals is to write them in set-builder notation. CCore ore CConceptoncept Set-Builder Notation Set-builder notation uses symbols to defi ne a set in terms of the properties of
[PDF File] Chapter 2 Set Theory (page 42 - ) - University of North Georgia
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• Specify sets using both the listing and set builder notation • Understand when sets are well defined • Use the element symbol property • Find the cardinal number of sets ... Example 5: Finding all subsets of a set Let 𝑺= {𝟎,𝟏}, 𝑻= {𝒂,𝒃,𝒄} and 𝑬= {𝟎, 𝟏, …
[PDF File] Section 1.1: Sets - Hobart and William Smith Colleges
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Set-builder notation is an explicit description of a set in terms of rules. Set-build notation has the following presentation: fexpression : rulesg: Example: The set of even integers = fn 2Z : n is eveng = fn : n = 2k;k 2Zg = f2n : n 2Zg: Notation Set-builder notation is an explicit description of a set in terms of
[PDF File] Welcome to CS103! - Stanford University
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We've got a big journey ahead of us. Let's get started! “CS103 students”. “All the computers on the Stanford network” “Cool people”. “The chemical elements”. “US coins” “Cute animals”. A set is an unordered collection of distinct objects, which may be anything (including other sets). , , , A set is an unordered ...
[PDF File] COURSE NOTES FOR MATH 540, HONORS LINEAR ALGEBRA
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It is important to practice translating, both ways, between set-builder notation and natural language descriptions of sets. One of the more unfamiliar feelings you may need to get used to is the need to name things, i.e., assign symbols to quantities. Example 1.6. (1)Set-builder notation to English: Describe in words, as naturally as possible ...
[PDF File] Math 8 — Functions and Modeling - University of California, Irvine
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For example, B = {a ∈A : 2 < a < 8} (the set of a in A such that a lies strictly between 2 and 8) In roster notation, B = {3,5,7}: plainly B is a subset of A. Can you express B in other ways using set-builder notation? 2This is enough for our purposes, though a course in set theory will convince you that this definition has its own problems.
[PDF File] Example sets problems (Katherine E. Stange, Math 2001, CU …
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22. Give set builder notation for the set of subsets Z which contain the element 0. Use symbols exclusively (not english words). 23. Give set builder notation for your favourite parabola, living in the Cartesian plane. Use symbols exclusively (not english words). 24. Give an example of set builder notation that represents the set {1}.
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