4. (a) Write down four distinct elements of the set {2 €C:2- E = 2i}.

Q: 2 Let A= then det(3A") = 6- -2 - 18 -6

A:

Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: 4. Give an example of a non-measurable subset of R. (witheutProof)

A:

Q: 1) Evaluate whether y, and y, are uncorrelated 2) Evaluate whether y, and y, are independent

A: Given, y1y2 = 111-1x1x2 So,  y1 = x1+x2y2 = x1-x2 And, Mean is 0 and Variance is 1 So, E(xi) =0…

Q: 2. Classify each set as closed, open, or neither. Justify your answer. A= {-+:nEN} E. 1-:] [0, 1)

A:

Q: If (0,1) ~ (-1,1) and (-1,1) ~ R. Deduce that (0,1) ~R

A:

Q: 2. Let, a, = 3, az = 4 and for n2 3, a, = 2a,-1 + an-2 + 5, express a, in terms of n.

A: Introduction: The disparities between every two successive terms in an arithmetic progression (AP)…

Q: TION 4 If A, B, C be three sets such that Au B = AUC and ANB = ANC, then : O B = C O A = C O A = B =…

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Q: Let feC-2,2], fo-o. Prove that Max -2

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Q: 9- Let X-U(0,8), then P(X> X²) is

A: Given that

Q: Create the logic circuit diagram for F= XY’ + XZ

A: Given problem Given that   F= XY’ + XZ

Q: 5. Give an example (by words) for a collection of objects which is not well defined

A: Given, We have to write an example for a collection of objects which is not well defined.

Q: Find a set of 3 points in S' so that dcos does not satisfy the triangle inequality.

A: The sine distance between two points x,y∈ℝ2 is defined as: dsinx,y=x.yxy and the cosine distance…

Q: 24) 100 people are surveyed, obtaining the following information: -Every respondent who owns a car…

A: Given that the total number of respondents is 100. There are 54 male respondents. The number of male…

Q: 3. Show that B = {0, 1, 2, 6, 9} is a difference set in Zjj. What are the parameters of the SBIBD…

A: For the given question ,t he first thing to do is to find the value of λ. Then, we will proceed…

Q: Let S = {-5, -1, 0,, 1, V5, 3, 5}. Determine which elements of S satisfy the inequality. 5. -2 - 3x…

A: Given inequality is,  -2-3x≥13 It is simplified as follows: -2-3x≥13-2-3x+2≥13+23x≥13+23x≥73x≥79

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: 4.2. Let S be the open set consisting of all points z such that |2| < 1 or |z – 2| < 1. Show that S…

A: Connected set: If any two points of a given set can be joined by a continuous polygon arc such that…

Q: 4. What value/s of c will make the set S = {(3, 5,-2), (3, c,-25), (1,–4, 7)} dependent?

A:

Q: IL Determine the Absolute V'alue of the following 6.-3 7-13-8) 9. 0-7 10. 9 11. 81-9 12. 43 13.-17

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Q: 4.1 Write down the identity element of the set and substantiate. 4.2 Write down the set of inverse…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for you…

Q: Describe the set S = { x : I 1/2x - 3 I &gt; 4} in terms of intervals.

A: S=x : 12x-3&gt;4

Q: -16] --14] Let ai -20|, a2 = -16 and az = –18 -4 -4 -4 The set {a1, a2, az} will span R' unless h =

A:

Q: 2.6 Using the Venn diagram to prove that (x1 + x2 + x3) • (x1 + x2 + x3) = x1 + x2

A: claim- use venn diagram to prove that  x1+x2+x3·x1+x2+x3=x1+x2 let x1  x2 x3

Q: 3. Show that if A-1 exists, then eAT dr = A-1(eAt – I) = (eAt – I)A-1.

A:

Q: 1 A class of 40 students was each required having three textbooks in each of Economics, Mathematics.…

A: Topic:- ven diagram

Q: 3. Show that Z, -

A:

Q: 1. Give at least 5 pairs of numbers a and b. For each of those pairs find at least 10 elements of…

A: We need to find at least 5 pairs of numbers a and b. For each of those pairs  at least 10 elements…

Q: 4.4 Find a set of 3 points in S' so that dcos does not satisfy the triangle inequality.

A: Please check step 2 for the solution.!

Q: 5) Compute the number of ordered pairs (x,y) with x>0 and y>0 that satisfy x+(y)=5.3 and y+(x)=5.7

A: In this question we have to find the number of ordered pairs (x,y).

Q: d) The set E = (-1,0) U (0, 1] is an open set. %3D

A: Given set is E = (-1, 0) ∪ (0, 1]

Q: 4) Describe the graph of the given set C o{ (x,y): ニ

A: Parametric curves: When we define the coordinates of the point x, y in terms of another variable,…

Q: Consider the word TORTOISE. Count the number of arrangements of this word (a) such that no two…

A: Consider the given word TORTOISE. The objective is to count the number of arrangements of this word:…

Q: Let S = {(x, y) E R X R: y - x = integer} List of four members of [-3]

A: GivenS=x,y∈IR×IR: y-x=Integernow-3=x∈IR: -3-x=Integernow, 1∈IR,2∈IR , 3∈IR and 4∈IRso the four…

Q: Let's generalize the situation in problem #1. Consider the relation < on the set [n] : {1,2,...,n}.…

A:

Q: ,- ). Show that there a 3,4

A:

Q: (b) Suppose that X,Y and Z are subsets of {1, 2, 3, . . . , 10} and |X| = |Y| = |Z| = 7. Deduce that…

A: Given X, Y and Z are subsets of 1, 2, 3,.......,10. Cardinality X=Y=Z=7. To prove that X ∩ Y ∩ Z is…

Q: Let S = {-4,-1,0,2/3,5/6,1,√5,3,5} determine which elements of S satisfy the inequality -2+3x ≥ 1/3

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Q: 5. Differentiate with respect to x: SET A. 5e

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Q: 13. Let S = {x eR : x20 and 2| x - 31+ Vx(Vx - 6) + 6 =0. Then, S (a) is an empty set (b) contains…

A:

Q: EX LeT X = {!,2,3,415,6} T- Ex,¢,てり,E4,しろ4), [ス456 Topology.?

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Q: What will be the cartesian product of three sets if one set of them is empty?

A: The answer is given as follows:

Q: 2. Let S be the set [9]: (1.2.9). (c) List 5 derangements of S having 2 in the 3rd position and 5 in…

A:

Q: C. Think of a set with m + n elements as composed of two parts, one with m elements and the other…

A: m+n elements as composed of two parts.

Q: 2. (i) Show that given finitely many countable sets A1, A2,, An, the set A1 x A2 x .. x An is also…

A: A set A is said to be countable if its cardinality is same as the set of natural numbers ℕ. If A and…

Q: 3. Suppose at a small college, 30% of the students are freshmen, and 60% of the students live on…

A: Given, The probability that the students are freshmen is pf=0.30 The probability that the students…

Q: A police department released the numbers of calls for the different days of the week during the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: If A and B are points in 3-space then |AB| = |BÁ| Select one: O True O False

A: If A and B are point in 3-space then

Q: 2.3 Show that the following sets don't satisfy the law of contradiction and the law of excluded…

A: part(a) GIVEN μAx=11+x TO SHOW: given function don't satisfy the following laws 1) law of…

Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .