) a function because the vertical line test only intersects the graph in one point

Q: In Section 1.2 we showed that ordered pairs can be defined in terms of sets and we defined Cartesian…

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Q: How many one-to-one functions are there from a set with five elements to a set with four elements?

A: The objective is to find the number of one-to-one functions is there from a set with 5 elements to…

Q: Describe the set of numbers that satisfy the following condition: -x is positive

A: the given condition is that -x is positive. this implies x is negative.

Q: Express the set of numbers x satisfying the given condition as an interval. |x| < 4

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Q: Come up with an open interval A and closed interval B such that A∪B = (1, 10] and A ∩ B = [4, 5).

A: our aim to find the examples satisfying A - open interval  B- closed interval  such that A∪B = (1,…

Q: Express the set of numbers x satisfying the given condition as an interval. |3x + 5| < 1

A: 3x+5<1

Q: 5. Which of the statements is Not a function.

A: A relation is the ordered pair of input and output values. A graph or a mapping diagram can be used…

Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

Q: Express the set of numbers x satisfying the given condition as an interval. |4x − 1| ≤ 8

A:

Q: (1,1),(2,2),(3,3)(4,4),(5,5) relation or function?

A: Given: R=(1, 1), (2, 2), (3, 3), (4, 4), (5, 5) To determine: Given set is a relation or function.

Q: es for which the points P(x, y) are on the g y <0 2- -2 -1 -2 3+ Write your answer in interval…

A: Topic:- function

Q: What is the natural domain?

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Q: Come up with an open interval A and closed interval B such that A∪B = (0, 4) and A ∩ B = [1, 2].

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Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove that the relationship is…

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Q: Describe the set of real numbers satisfying Ix - 31 = Ix - 21 + 1 as a half-infinite interval.

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Q: Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural…

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Q: can two disjoint sets be close? Justify your answer using an example.

A: We know that any closed interval of the form [a,b] is an closed set. We use this fact further.

Q: Express the set of numbers x satisfying the given condition as an interval.        I x -4 I &lt; 2

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Q: Describe the set of real numbers satisfying |x − 3|=|x − 2| + 1as a half-infinite interval.

A: Solve the equation: x-3=x-2+1 for x. Subtract x-2+1 both sides. x-3-x-2-1=0. Since,  x-3=    x-3…

Q: Express the set of numbers x satisfying the given condition as an interval. |x| ≤ 9

A: Given: x≤9 Formula Used: z≤a, a&gt;0 then -a≤z≤a

Q: 18. What can you deduce about the sets X and Y if you know, a. there is an injective function f: X…

A: Given that two sets X and Y.a)There is an injective function

Q: Check whether each satisfy a relation property: (ex, transitivty, etc ): > = " < 9 for real numbers

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Q: Let A = {a, b, c, d} and f = { (a, 0), (c, 12), (d, 18), (b, 12) }. Is f a function from A to B ?…

A: Given, A = {a,b,c,d} f = {(a,0) , (c,12) , (d,18) , (b,12)}

Q: Give an example of a function f : (X1, d1) → (X2, d2) that sends compact sets to compact sets, but…

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Q: a Prove that the interval [-1, 2] is a closed set in R. Explain each step in your argument.

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Q: Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X1, X2, X3, X4 = {0, 1}}. Show that x₁…

A: (a) It is given that x=x1,x2,x3,x4 such that 93x1+34x2+26x3+18x4≤131 and x1,x2,x3,x4∈0,1. So, the…

Q: Give a proof of the following statement. Suppose A, B and C are sets, f is a surjective function…

A:

Q: A relation R exists such that for every input(x) is 2x. Is relation R a function, and why (20…

A: Solution - Option C is correct, "The relation R is a function because there is only one output for…

Q: If f A —> B and g : B —> C are injective function, then gof: A —> C is an injective function. Prove…

A: Given that f: A→B is given injective. this implies cardinality of set A is less then cardinality of…

Q: A relation consists of all the points in the x-y plane that are either on the line y=1 or the line…

A: Here, the objective is to determine if equation represent a function.

Q: True or False A function is a relation between two sets Dand R so that each element x in the first…

A: By definition: A function is a relation from a set of inputs to a set of possible outputs where each…

Q: Prove this: There is a one-to-one correspondence between any line and the set of real numbers.

A:

Q: WHICH OF THE FOLLOWING BEST DESCRIBES THE RANGE OF THE RELATION: 8- ·기 -5 -4 -3 -2 -1 *9 -8 678 9 -2…

A: The graph is given as follows:

Q: express the set of the numbers x satisfying condition |x-1| &lt; 18 as an interval

A: The condition |x-1|&lt;18 is rewritten as,

Q: i) show that a closed interval is a closed set;

A: Note: According to bartleby we have to do only first question please upload the question separately.…

Q: Find a function from the set {1,2,.....30} to {1,2,.....10} that is a 3-to-one correspondence.

A:

Q: (d) Justifying your answer, find the smallest set of related pairs which must be added to R in order…

A: We know that a relation is called an equivalence relation if it is reflexive, symmetric and…

Q: What is the domain of the relation (8, 2), (6, 4), (4, 2), (2, 4)? O 2,4 O 2, 4, 6, 8 O 6, 8 O 2, 4,…

A: Concept: Domain is the set of all first elements of ordered pairs (x-coordinates).

Q: State the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric,…

A: Reflexive relation: A relation R is reflexive over element X if every element X is related to…

Q: Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder…

A: Set: In set builder notation the real number between 2 and 7 but not including both the numbers, Let…

Q: Let RC R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given problem is :

Q: Define a relation ~ on the set of real numbers by X~ y means | x |+|y|=|x+y|. Determine whether - is…

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Q: From the topic of Euclidean and Metric Spaces: Real Analysis Provide ALL the conditions if…

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Q: What is an injective function from a set A into a set B?

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Q: Define a relation Pfrom R+ to R as follows: For all real numbers x and y with x> 0, (x, y)E P means…

A: Introduction: A relation is a subset of Cartesian products of two sets. In each ordered pair, there…

Q: Express the set of numbers x satisfying the given condition as an interval. |x − 4| &lt; 2

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Q: If X = {-2,-1 ,0 ,1,2} and Y = {4 ,2 ,, } and R is a relation from X to Y where "a R b" means "b 2"…

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Q: Give an example of a relation. Which is(i) Symmetric but neither reflexive nor transitive.(ii)…

A: i. Symmetric but neither reflexive nor transitive.

Q: Show that the translate of an Fδ set is also Fδ.

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Q: One of the following inegualities holds for every xand y belong to real numbers R. اختر احدى…

A: