O cf AandB are subsets of X such that A=R 3. then fiA = {cB but the converse is not tiug

Q: 5. For the set C = {4, 5, 6, ....} is it true or %3D false that 7 e C? True False

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Recall that P(n, r) is the number of r-permutations of an n-element set. Prove the following…

A:

Q: 1. Decide whether the following stabe ments false . Justify are true or (a) YxeTR, VyeR, x²-y² z…

A: (d) True We have to show that,  ɸ⊆ϕ Let a Set A which is the subset of ϕ, i.e A⊆ϕ therefore it will…

Q: f Applyth) oroterAunge -kutta to sotve the fotloing Vatue probtem and 1

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Q: 1. A is a well defined collection of 2. objects called 3. If A and B are sets, then B C A iff In tho…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: Let C: z-3 and I – 6dz. ONone of these

A:

Q: Suppose is dhe iavene faction of a diffarentiable šunc- tica fand let Glu) -1/r . E3) - 2 and /3) -…

A: G(x)=1f-1(x)f(3)=2 , f'(3)=1/9

Q: For Aand B subsets of formal A x CBU C) is a se t x iprovide subset

A:

Q: Let S be a nonempty subset of R. If sup(-2S) = 10, then %3D O a. sup(S) = 5 O b. inf(S) = -5 Oc.…

A:

Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: Prove: If = ¿ (where a, b, c, and d are nonzero), b then d*

A: Given:               ab=cd  (where a,b,c  and d are non zero.)

Q: Let X ∼ Bin(n, p), and let Y = n − X. Show that Y ∼ Bin(n, 1 − p).

A: Here X follows Binomial with parameters n and p. Here, Y=n-X. Then Y takes the values n-0, n-1,…

Q: Jin Let G beagreupsuch that I6tefs thens

A: Answer

Q: Let D be a set of dogs, R a set of retrievers, and G a set of golden retrievers. Assume that GCR and…

A: a) Given that G⊆R and R⊆DIf, G≠R≠D then we can say that there are some dogs which are not…

Q: Let A, B be any sets with ACB. Then O None of these O IP(BxB)|s|P(A×B)| O IP(A×B)=|P(B×B) O…

A:

Q: Let D be digraph. If id(x) > 0 for all x ∈ V (D), then D contains a circuit.

A: Given:- Let D be digraph. If id(x) > 0 for all x ∈ V (D)

Q: 3. Are the following sets countable or uncountable? Justify your answer with a proof. (a) {2" |n e…

A:

Q: How many ways Com you orenge lo buks bokishelfthat fhes Apace for that has space for only on a 5…

A: This is the problem of permutation and combination. So, there are 5 places for 10 books on the…

Q: Determine whcther cach of the following sets is well-ordercd: (i) the set A = {: (neQ)^(n > 0)};…

A: When every non-empty subset contains the least element, the relation is referred to as well-ordering…

Q: Let z-2 z-2 n st pC& >0.5)20.9 and y:bin (n,o.38), find or

A: Y~Binomialn, 0.38 Compute the mean and the standard deviation of Y using the formulae: Y=np…

Q: Given the following sets, what is A U B?  U={x│0≤x≤20}         A={2x│0≤x≤5}…

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

Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

A:

Q: Q Let 8=R and Prove disprove that zis atopdagy or on R.

A:

Q: Let S be a 50-element subset of {1, 2, 3,...,87} and let T = {s+11 :sE S}. Prove that SnT+ Ø.

A: This is a question of Set theory, application of the Pigeon Hole Principle.

Q: Let'Y be the set of f bleod types B+ Hat type Connot donate blood to.

A: Here, X is the set of blood types AB- can donate blood. AB- can donate blood to AB- and AB+ Hence,…

Q: Prove S^2 is simply connected.

A:

Q: Apply any method to prove that a|b (or a nand b), which is defined to be ¬(a ^ b) is complete. Write…

A: The NAND & NOR gates are called universal gates as they perform all the logical operations of…

Q: Consider the following subset S C R 1 -3 S = -2 -10 8 Is span(S) = R*? Explain your reasoning and…

A: See the attachment

Q: w that the set S = 3 6. 4 5 ms all of R³ or find an element of R³ not belonging to span(S).

A:

Q: 4.2. Let a, b E Z, where a 0 and b 0. Prove that if alb and bla, then a = b or a = -b. -b.

A:

Q: of studends, 65 play toot bell, 25 play football Anagmmp goup. us play hockoy, 42 play'Crickot, 20…

A: Let F , H and C represents the number or set of students who plays football , hockey and cricket…

Q: .....………., ɑn are in A.P., where a; > 0 for all i, show that : 1 If a1, a2, a3, 1 1 n- 1 %3D Va1 +…

A:

Q: 3. Use the diagram below to prove AQUT ASUP,

A: Please refer the attached image for complete solution.

Q: If AB is a subset  of C,  show that P(C)≥P(A)+P(B)-1. Please show me all of your work.

A: Given that; A∩B⊂C⇒C⊃A∩B⇒P(C)≥P(A∩B)

Q: Let A1, A2, ... , An be any n sets, n 2 1. Show that (U-1 Ar) = U=1 Ar %3D

A:

Q: 2) Let mf lu and (a,m)=| a,bE Z such that Let h= Om ( a) show and and (h,m)=1, %3D let. ne OmCab)…

A:

Q: 3. Prove or disprove: If a | (b + c), then either a |b or a | c. h of the follo

A: Since you have asked for question number 3 , we have solved it for you.

Q: Let X + 0, |X|> 2. Then (X, Tna) is not To -space. Select one: True O False

A:

Q: the followiny Qu:- proof O Csch (X)= In Că

A: Note:-   as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: (4.1) For sets A and B. prove that P(AB) = P(A)~P(B).

A:

Q: Consider the following sets A = {1,2,3.4,5} and B = {2,3.4}. Which of the following is NOT TRUE? * A…

A: The given sets are          A= {1,2,3,4,5}  and B= { 2,3,4} 1)If two sets are said to be joint set…

Q: Suppose that r, s are integers (possibly different from x, y res that ar + bs = c. Show that there…

A: Introduction: Let us suppose that two integers are a and b, greatest common divisor of these two…

Q: Let C= {[c, d] : –1<c<d< 5} be the family of subsets of R, where [c, d] = {x E R: c< x< d}. (a)…

A:

Q: Let : fiaiy) = x@y? (12-x-y) the lon diti on Shon that C169ラ (hi2)t

A: Given that, fx,y=x3y212-x-y, x&gt;0, and y&gt;0. To prove, fx,y≤6912. The given function can be…

Q: If A subut of B. where B 18 a closo d subset of IR show that

A: Given: A is a subset of B, where B is closed subset of ℝp. To show: A¯⊆B.

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”.