A realation pis defined on set Z, a set of all integers, such that p= {(1, y) EZ x Z:Y-I is divisible by 5). Discuss whether pis an equialence relation. IF A = {z E Z:(2, r) E p, – 10

Q: 1. If f is a function on a set A = {1,2,3,4,5} such that f = {(1,2), (2,3), (3,4), (4, x), (5,5)}.…

A: Answer C

Q: Question 33 With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is…

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Q: Question 35 For the binary relation R (defined below) on A and each tuple (a, 6) indicating that a…

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Q: Let R be the relation defined on P({1,..., 100}) by ARB if and only if |An Bl is even. Is R…

A: Given: R is the relation defined on P1,....,100 by A R B.           A∩B is even.We need to check…

Q: Let x be the set of all positive integers and d(min) = | = - = | show that (x,d) is not complete

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Q: Determine if 0 >=(61-6-J-RA) is in the span of = 0

A: Given: -1225 To check:If -1225 is in the span of Φ=1100, 1001, 0110, 0011 or not.

Q: Pzif akb then [a,b]-(- All of a,b are in real numbers

A: The given statements are: p: a<b q: a, b=(-∞, b] \ -∞, a Prove: If p, then q. If a<b, then  a,…

Q: Let A = {1, 2, 3) and B = {4, 9, 21, 25). Define the relation R from A to B by a R b if a divides b.…

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Q: Let A = {1, 2, 3, 4, 6}. Let R be therelation on A defined by {(a, b): a , b ∈A, b is exactly…

A:

Q: Let Z be the set of integers, determine f:Z->Z, such that, for all integers a and b,…

A:

Q: Investigate if the following relationship 'is' or 'not' of order a ۲b ⟺ a ≤ b +1, a, b ∈ Z

A: A relation R on a set X is said to be order relation if it satisfies the following conditions,…

Q: Let Ω-set of all real numbers, A-index set. Identify the generalized union and intersection of the…

A: Given: Ω set of all real numbers To find: Solution

Q: Let A, B s R (R represents the real numbers) and A, B both non-empty. Define A + B = {a+b: aEA and…

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Q: ) Let Z denote the set of all integers. Determine whether each of the relations on Z given below are…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: x + y)(z + w) = xz + xw + yz + yw A.) Explain in your own words what this problem is asking. B.)…

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Q: 3. A = {2, 2+2, 2+4,2+6, 2+8} where A = {2,4,6,8} 4. A=(1-22, 1+22) where A = Z*

A: Note : (i) ∩α∈S Aα=x : ∀α∈S ,x ∈Aα               (ii) ∪α∈S Aα=x : ∃α∈S ,x ∈Aα

Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

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Q: Determine if the relation R on the set of all integers is reflexive, symmetric, or transitive, where…

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Q: Show that if x,y,z,w are real numbers such that x < y and z ≤w, then x + z < y + w.

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Q: n Question 3 For the relation R on the set of integers, where xRy if x is a factor of y, select all…

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Q: K Match each function to its domain from the list below. Some domains may be used more than once,…

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Q: A is a non-empty set. Show that the power set of A is in one to one correspondence with the set of…

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Q: let G be the set of all triples of the form (k1, k2,1) or (k1,k2,-1), where the ki, i=1,2 are…

A: Given :  G = k1, k2, ±1 : k1, k2 ∈ℤ with the operation  k1, k2, 1l1, l2, -1 = k1+l2, k2+l1, -1 To…

Q: 5. Let x and y be irrational numbers such that x-y is also irrational. Define sets A and B by A = {x…

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Q: Which of the following sets is not closed for the operation °, which is defined by the rule a°b = a…

A: Option (a) is not closed under the operation °.Option (b), (c), and (d) are closed under the…

Q: (c) z-y is an integer A. Reflexive B. Symmetric C. Transitive D. None of the above (d) x+y=0 A.…

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Q: 5. A = {0, 32, 62} where A-Z* 6. A = [5, 10-] where A = Z¹

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Q: 5) Let R be a binary relation over the positive integers defined as follows: R = {(a, b) | 2b < a <…

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Q: Determine all functions f from the set of posit that, for all positive integers a and b, there…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.