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.

Q: b) BCA iff A n B = ¢ c) (A – B) U B = A iff B C A

A:

Q: 2. Let A = {r|x is older than 25}, B = {y|y_is older than 50}, C = {z |z is between 20 and 30}. Draw…

A: The question is related to sets. The solution is explained below.

Q: To prove: For all sets A and B, if B C A° then AN B = Ø. I must: Suppose that BC A and AN B+ Ø.…

A:

Q: Let a, b, c e Z. show that ca & cb if and only if c (a, b).

A:

Q: Let A, B, C be sets. Prove (AAB) -C = (A- (BUC))U(AN BnC)

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Q: Suppose A and B are sets. Au B = B if and only if As B. True False

A: Given statement is A and B are two sets. A∪B=B if and only if A⊆B. We know that if A⊆B and B⊆A then…

Q: • Show that if D is a set and E is a closed set containing D, then E must contain ƏD, i.e., the…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Let A and B be sets. 1) If |A| = 10, |B| = 24, and |A n B| = 4, then |A U B| = || %3D 2) If |A U B|…

A:

Q: Let A and U = H. Then A2017U is equal to

A: The given matrix is A=-120-1 find A2=-120-1-120-1=1+0-2-201=1-401 therefore A2=1-401 similarly…

Q: Determine whether the set S = {1, x², 3 + x²} spans P2. O S spans P2. O s does not span P2.

A: Consider the given set S. S=1,x2,3+x2 Now, make the matrix from the given set. 103000011

Q: 4. In each case, sketch the closure of the set: 1 (c) Re (d) Re(z?) > 0.

A: Given:

Q: Let A, B, and C be sets. 1. Prove: If A C B then ANC C BnC. 2. Disprove: If AnC CBNC, then A C B. 3.…

A:

Q: Prove that if A – B – D and B – C – D, then A -C– D.

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Q: prove that: DO e de a e +6 2/3 cwhere a, b > o

A: Where a, b>0

Q: d set): Let (M ,d) be a (SUT)' = S' U T'.

A:

Q: For sets A and B, prove that AU (B - A) = B

A:

Q: Let U = {x | x is a letter in the word %3D GUADALARAJA}, where this is the universe set. Also, let M…

A:

Q: If sup A < inf B for sets A and B, then there exists a c€R satisfying a <c<b for all a EA and bEB.

A:

Q: Let A, B, and C be sets. Prove A × (BnC) = (A × B)n (A × C).

A:

Q: Assume that AA and BB are disjoint subsets of UU, and that n(U)=55n(U)=55, n(A)=23n(A)=23, and…

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Q: Let A = {2n : n e N}, and B = {n E Z : n² is even}. Neither set is a subset of the other. O AC B. O…

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Q: (10) Show that the set A = {a € Q : a² < 2 or a < 0} is a %3D cut.

A:

Q: Prove the following theorem directly. 'Let B, E,W be sets. If B Ɔ W, then BU E WUE"

A: Given B, E and W are three sets .

Q: (d).Show that the derived set E′E′ of any set EE is closed.

A: To show that derived set E′ of any set E is closed.

Q: Let A, B and C be sets. It is given that AUC= BUC and AnC= BnC. Shơw that A = B.

A:

Q: Show that the sete S = {x E R]x = m/3, where m E N with m > 4} is countable

A:

Q: Prove: Va,b,ce Z, if a|b and a|c then a|(b-c)

A: ab  &amp;  ac This means that b &amp; c are multiples of a. ⇒b=a·k  &amp;  c=a·m     where k, m∈Z

Q: Recall that for a set S, P(S) is its power set. Given two sets S and T, prove that S C T if and only…

A: Let S and T be two sets and P(S), P(T) are its power sets.Power set of a set is defined as the…

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: Prove that if E,ak A and E bk = B then (a) E=1cak cE=1ak = cA (b) (ak + bx) = Eak + E,bk = A+ B 'k=1…

A:

Q: If the sets A, are independent and P(U, A,)=1 then P[A i.o.] = 1. %3D

A: Let {An}n=1∞ be an infinite event satisfying P(An)&lt;1 for all n, then  P∪n=1∞An = 1 if and only if…

Q: Let a, b, c E Z. show that ca & cb if and only if c (a, b).

A: Division properties are used to prove it

Q: With help of Venn diagrams show that the following are indeed true: a.X n (Y U Z) = (X n Y) U (X…

A:

Q: 2. Determine whether the set S = spans M22-

A: Let A=1ab0, B=a01c, C=0ca1 and D=b1ac. Substitute a =6, b =5 and c =1 in above matrices. A=1650,…

Q: Let c= and D= [7 -1 -2]. 1 - 6 Find CD if it is defined. Other.se, tap on "Undefined". CD = [00)

A: The given matrices are C=04-6 and D=7-1-2

Q: Suppose that (x, y) E (A \ B) × C, for sets A, B,C C S. Then a E A and r¢ B, and y E C. This implies…

A: Use the following definitions, to prove the given result. Let A and B be two sets. The Cartesian…

Q: Indicate whether the following statement is true or false? 1. If S = span{u1, u2, uz}, then dim(S) =…

A:

Q: Set C and the universal set U are defined as follows. U={p,q,r,x,y,z} C={p,q,x}

A: Given,        Set C and the iniversal set U are defined as follows :         U=p,q,r,x,y,z…

Q: 1. Suppose A, B, and C are sets, A. Prove that: AX (Bn C) = (A X B) n (A x C) %3D

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Given the following sets X= {a,b,c} Y= {a} Z= {a,d} In the universe U= {a,b,c,d,e}, what is (X’…

A: Sample Space (SS): The total number of possible outcomes of an event is called Sample Space and it…

Q: eld of subsets of 2 and suppose Q: B [0, 1] is a set dditive on B. 1 for all A e B and Q(2) = 1.…

A: Complete proof is provided in step2.

Q: The set Dom(R)={a_eA: (b; a) e Rfor some b eB}is called the domain of R Ture False O

A: Domain is the input values of any relation and range is the output values of the relation.

Q: Suppose A, Band C are finite sets of integers. Decide whether each of the following is a set, a…

A:

Q: Let A and B be two finite sets such that |A| = 20, |B| = 28 and |A U BI

A: Given A=20B=28A∪B=36

Q: Let A={x,y,z,1} and let B= {1,2,4}. If a set  U= (A x B) U (B x A), how many elements are there in…

A: Recall the following facts.

Q: Let a,b,c be intergers with gcd(a,b)=1 and c|(a+b) (c divides a+b). Prove that gcd(a,c)=1 and…

A:

Q: 3A, B E {sets} such that A CBAA= B.

A: To check whether the given statement true or false: ∃A,B∈sets such that A⊆B∧A=B

Q: Determine whether the set S = {1, x², 9 + x²} spans P2. %3D O S spans P2. O s does not

A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…

Q: .Which of the following sets is countable and which is uncountable: A = {x |x = 2n, n e N} B = {x |…

A: We will find out the required values.

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.