Let X be an ordered set, and A C X. Show that a. for every E X, x has at most one immidiate successor and at most one immediate predecessor. b. Show that A has at most one smallest element and at most one largest element.

Q: 1. If S is a nonempty set of real numbers and x = inf S, show that for each &> 0, there is an a ES…

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Q: this question and subsequently, let a₁, A2,..., a5 denote these numbers: 2,2,1,7,3 Let X denote the…

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Q: A set D C RP is disconnected if and only if D = EU F, where E, F are non-empty and EnF= ø,EnF = Ø.

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Q: (d) List all outcomes in the event D that exactly two vehicles go in the same direction. D = (e)…

A: See the handwritten solution

Q: Theorem 5.25. Let A, B, and C be sets. Then 1. A× (B N C) = (A × B) N (A × C) 2. A × (B U C) = (A ×…

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Q: also compute η2 for a. and r2 for b.

A: Eta square measure the effect size of the observations. It is calculated by the combined value of…

Q: 6. Let X and Y be subsets of {a,b}. Write the relation where X is related to Y if |X| = |Y| as a set…

A: Let  A={a ,b }  Cardinality of A=2 so the cardinality of power set is 2^2 =4 Now power set of A is…

Q: C. Draw a Venn Diagram showing the number of students in each of the eight sections of the Venn…

A: Note: as per guidelines we support only three subparts of the questions.kindly repost next question…

Q: a. Let a Z, then a² - 5a +7 is odd.

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Q: Let S = (a, b, c, d, e, f with P(b) = 0.16, P(c) = 0.12, P(d) = 0.29, P(e) = 0.22, and P(f) = 0.11.…

A: Given S = { a, b, c, d , e , f } P( b ) = 0.16P( c ) = 0.12 P( d ) = 0.29 P( e ) = 0.22 P( f ) =…

Q: 1. Let A, B, and C be sets such that An BnC + Ø. Draw a Venn diagram for each of the following set…

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Q: graph the complement of the following set S={ (x,y) l 2x+3y>=12

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Q: Determine whether each of the following is a unary operation on the given set. a. h(x) == on N b.…

A: A unary operation is an operation that takes a single input and produces a single output.Then the…

Q: 6.3.6 For each real number x, let Ay = {3, –2} U {y E R : y > x}. Find U Ax and N Ax. xER xER

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Q: EXERCISE 4.2.9. Let P be the set of people in a group, with |P| = p. Let C be a set of clubs formed…

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Q: jim has precisely 150 followers. and, all 150 people who follow jim have precisely 150 followers. In…

A: Given that Jim has 150 followers and a follower of Jim follows Jim and 149 others. Let the set S is…

Q: Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.25, P(d) = 0.2, P(e) = 0.1, and P(f) = 0.11.…

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Q: 2. Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4). (a) How many ordered pairs are in S × T? T × S? (b)…

A: 12. Given that,                    S=0, 1, 2, 3, 4  & T=0, 2, 4.

Q: Consider a set S={1,2,3,4,5} and P(x)=x−110, where x is a member of S. Calculate E(S).

A: It is given that P(x)=(x-1)/10.

Q: Compute T B2

A: Given: B=1-1-11 and T:ℝ2,2→ℝ2,2 defined by T(A)=AB-BA. Also, B2=1001, 0110, 100-1, 01-10 To find:…

Q: We know that if E is a measurable set, then each translate E + y of E is also measurable. How about…

A: If E is a measurable set, then each translate E+y of E is also measurable.