Question and Answers Forum

Set TheoryQuestion and Answers: Page 5

Question Number 64250 Answers: 0 Comments: 0

Question Number 56744 Answers: 1 Comments: 0

If R be a relation on a set of real number defined by R={(x,y): x^2 +y^2 =0}, find i− R in roster form ii−Domain of R iii−Range of R

$$\mathrm{If}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{relation}\:\mathrm{on}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{real}\:\mathrm{number} \\ $$$$\mathrm{defined}\:\mathrm{by}\:\mathrm{R}=\left\{\left(\mathrm{x},\mathrm{y}\right):\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{0}\right\}, \\ $$$$\mathrm{find}\: \\ $$$$\:\:\mathrm{i}−\:\mathrm{R}\:\mathrm{in}\:\mathrm{roster}\:\mathrm{form} \\ $$$$\:\:\mathrm{ii}−\mathrm{Domain}\:\mathrm{of}\:\mathrm{R} \\ $$$$\:\:\mathrm{iii}−\mathrm{Range}\:\mathrm{of}\:\mathrm{R}\: \\ $$

Question Number 56203 Answers: 0 Comments: 0

Question Number 55633 Answers: 1 Comments: 0

Known set A⊆R not empty, If Sup A=Inf A, then set A is..

$$\mathrm{Known}\:\mathrm{set}\:{A}\subseteq\mathbb{R}\:\mathrm{not}\:\mathrm{empty}, \\ $$$$\mathrm{If}\:\mathrm{Sup}\:{A}=\mathrm{Inf}\:{A},\:\mathrm{then}\:\mathrm{set}\:{A}\:\mathrm{is}.. \\ $$

Question Number 47354 Answers: 0 Comments: 4

Question Number 45840 Answers: 0 Comments: 0

a≦7⇒P(!∃x_a )=0, b≦9⇒Q(!∃y_b )=0 for a, b∈N And A⊋A′: A={(x, y)∣P(x)∙Q(y)=0}=A′, B_(∈A) ={(x, y)∈A∣x=y} Then ∀t∈N: ∣B∣=n(t)=f(P(x), Q(y)), also only t can be in [N, M]. find M. :(

$${a}\leqq\mathrm{7}\Rightarrow\mathrm{P}\left(!\exists{x}_{{a}} \right)=\mathrm{0}, \\ $$$${b}\leqq\mathrm{9}\Rightarrow\mathrm{Q}\left(!\exists{y}_{{b}} \right)=\mathrm{0}\:\mathrm{for}\:{a},\:{b}\in\mathbb{N} \\ $$$$\mathrm{And}\:{A}\supsetneq{A}':\:{A}=\left\{\left({x},\:{y}\right)\mid\mathrm{P}\left({x}\right)\centerdot\mathrm{Q}\left({y}\right)=\mathrm{0}\right\}={A}', \\ $$$${B}_{\in{A}} =\left\{\left({x},\:{y}\right)\in{A}\mid{x}={y}\right\} \\ $$$$\mathrm{Then}\:\forall{t}\in\mathbb{N}:\:\mid{B}\mid={n}\left({t}\right)={f}\left(\mathrm{P}\left({x}\right),\:\mathrm{Q}\left({y}\right)\right), \\ $$$$\mathrm{also}\:\mathrm{only}\:{t}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\:\left[{N},\:{M}\right]. \\ $$$$\mathrm{find}\:{M}. \\ $$$$:\left(\right. \\ $$

Question Number 44826 Answers: 2 Comments: 0

Let A and B be sets. Prove that A = B if and only if A ∪ B = A ∩ B

$$\mathrm{Let}\:{A}\:\mathrm{and}\:{B}\:\mathrm{be}\:\mathrm{sets}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:{A}\:=\:{B}\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:{A}\:\cup\:{B}\:=\:{A}\:\cap\:{B} \\ $$

Question Number 42763 Answers: 0 Comments: 1

For A = {1, 2, 3}, let B be the set of 2−element sets belonging to P(A) and let C be the set consisting of the sets that are intersections of two distinct elements of B. Determine C P(A) = power set of A

$$\mathrm{For}\:{A}\:=\:\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3}\right\},\:\mathrm{let}\:{B}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{2}−\mathrm{element}\:\mathrm{sets} \\ $$$$\mathrm{belonging}\:\mathrm{to}\:{P}\left({A}\right)\:\mathrm{and}\:\mathrm{let}\:{C}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{consisting}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sets}\:\mathrm{that}\:\mathrm{are}\:\mathrm{intersections}\:\mathrm{of}\:\mathrm{two}\:\mathrm{distinct}\:\mathrm{elements} \\ $$$$\mathrm{of}\:{B}.\:\mathrm{Determine}\:{C} \\ $$$$ \\ $$$${P}\left({A}\right)\:=\:\mathrm{power}\:\mathrm{set}\:\mathrm{of}\:{A} \\ $$

Question Number 36061 Answers: 1 Comments: 2

Question Number 35703 Answers: 1 Comments: 0

Question Number 33551 Answers: 1 Comments: 1

Question Number 31711 Answers: 0 Comments: 0

Given p is primes and A={−(m/n)−p(n/m) ∣ m , n ∈N} find sup A

$$\mathrm{Given}\:{p}\:\mathrm{is}\:\mathrm{primes}\:\mathrm{and}\:\mathrm{A}=\left\{−\frac{{m}}{{n}}−{p}\frac{{n}}{{m}}\:\mid\:{m}\:,\:{n}\:\in\mathbb{N}\right\} \\ $$$$\mathrm{find}\:\mathrm{sup}\:\mathrm{A} \\ $$

Question Number 31669 Answers: 0 Comments: 0

A={(m/n)+((8n)/m) : m, n ∈ N} N= natural numbers supremum ? infimum?

$$\mathrm{A}=\left\{\frac{{m}}{{n}}+\frac{\mathrm{8}{n}}{{m}}\::\:{m},\:{n}\:\in\:\mathrm{N}\right\}\:\mathrm{N}=\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\mathrm{supremum}\:? \\ $$$$\mathrm{infimum}? \\ $$

Question Number 31237 Answers: 0 Comments: 3

Show that A−B = B′ ∩ A.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{A}−\mathrm{B}\:=\:\mathrm{B}'\:\cap\:\mathrm{A}. \\ $$

Question Number 29014 Answers: 0 Comments: 3

Prove that A∪A^c =A

$${Prove}\:\:{that}\:{A}\cup{A}^{{c}} ={A} \\ $$

Question Number 28806 Answers: 1 Comments: 0

If n(A)=15 and n(B)=25, (a) What are the greatest and least values of n(AuB)? (b) What are the greatest and least value of n(AnB)? (c) Draw Venn diagrams to illustrate the four situations in (a) and (b) above

$$\mathrm{If}\:\mathrm{n}\left(\mathrm{A}\right)=\mathrm{15}\:\mathrm{and}\:\mathrm{n}\left(\mathrm{B}\right)=\mathrm{25},\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{and}\:\mathrm{least}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\left(\mathrm{AuB}\right)? \\ $$$$\left(\mathrm{b}\right)\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{and}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\left(\mathrm{AnB}\right)? \\ $$$$\left(\mathrm{c}\right)\:\mathrm{Draw}\:\mathrm{Venn}\:\mathrm{diagrams}\:\mathrm{to}\:\mathrm{illustrate}\:\mathrm{the}\:\mathrm{four}\: \\ $$$$\:\:\:\:\:\:\:\mathrm{situations}\:\mathrm{in}\:\left(\mathrm{a}\right)\:\mathrm{and}\:\left(\mathrm{b}\right)\:\mathrm{above} \\ $$

Question Number 25723 Answers: 0 Comments: 0

Given a_1 , a_2 , ..., a_n are non−negative integers and satisfy (1/2^a_1 ) + (1/2^a_2 ) + ... + (1/2^a_n ) = (1/3^a_1 ) + (2/3^a_2 ) + ... + (n/3^a_n ) = 1 If n is positive integer, find all possible solution of n

$$\mathrm{Given}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:...,\:{a}_{{n}} \:\mathrm{are}\:\mathrm{non}−\mathrm{negative} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{satisfy} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{2}} } }\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{{n}} } }\:=\:\frac{\mathrm{1}}{\mathrm{3}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{2}}{\mathrm{3}^{{a}_{\mathrm{2}} } }\:+\:...\:+\:\frac{{n}}{\mathrm{3}^{{a}_{{n}} } }\:=\:\mathrm{1}\: \\ $$$$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solution} \\ $$$$\mathrm{of}\:{n}\: \\ $$

Question Number 24930 Answers: 1 Comments: 0

a+a=

$${a}+{a}= \\ $$

Question Number 24366 Answers: 1 Comments: 1

Given the 7-element set A = {a, b, c, d, e, f, g}, find a collection T of 3- element subsets of A such that each pair of elements from A occurs exactly in one of the subsets of T.

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{7}-\mathrm{element}\:\mathrm{set}\:{A}\:=\:\left\{{a},\:{b},\:{c},\right. \\ $$$$\left.{d},\:{e},\:{f},\:{g}\right\},\:\mathrm{find}\:\mathrm{a}\:\mathrm{collection}\:{T}\:\mathrm{of}\:\mathrm{3}- \\ $$$$\mathrm{element}\:\mathrm{subsets}\:\mathrm{of}\:{A}\:\mathrm{such}\:\mathrm{that}\:\mathrm{each} \\ $$$$\mathrm{pair}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{from}\:{A}\:\mathrm{occurs}\:\mathrm{exactly} \\ $$$$\mathrm{in}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{subsets}\:\mathrm{of}\:{T}. \\ $$

Question Number 22162 Answers: 1 Comments: 0

use the appropite set law to show that (A−B)∪(B−A)=(A∪B)−(A∩B)

$${use}\:{the}\:{appropite}\:{set}\:{law}\:{to}\:{show}\: \\ $$$${that} \\ $$$$\left({A}−{B}\right)\cup\left({B}−{A}\right)=\left({A}\cup{B}\right)−\left({A}\cap{B}\right) \\ $$

Question Number 22161 Answers: 0 Comments: 1

The students were asked whether they had dictionary(D) or thesau rus(T) in their room.the results showed that 650 students had dict ionary,150 did not had dictionary, 175 had a thesaurus,and 50 had neither a dictionary nor a thesaur us,fimd the number of student who (i)live in domitory ( ii)have both dictionary and thesaurus (iii)have only thesaurus

$${The}\:{students}\:{were}\:{asked}\:{whether} \\ $$$${they}\:{had}\:{dictionary}\left({D}\right)\:{or}\:{thesau} \\ $$$${rus}\left({T}\right)\:{in}\:{their}\:{room}.{the}\:{results}\: \\ $$$${showed}\:{that}\:\mathrm{650}\:{students}\:{had}\:{dict} \\ $$$${ionary},\mathrm{150}\:{did}\:{not}\:{had}\:{dictionary}, \\ $$$$\mathrm{175}\:{had}\:{a}\:{thesaurus},{and}\:\mathrm{50}\:{had} \\ $$$${neither}\:{a}\:{dictionary}\:{nor}\:{a}\:{thesaur} \\ $$$${us},{fimd}\:{the}\:{number}\:{of}\:{student}\:{who} \\ $$$$\:\:\left({i}\right){live}\:{in}\:{domitory} \\ $$$$\:\:\:\left(\:{ii}\right){have}\:{both}\:{dictionary}\:{and}\:{thesaurus} \\ $$$$\:\:\left({iii}\right){have}\:{only}\:{thesaurus} \\ $$$$ \\ $$

Question Number 21588 Answers: 0 Comments: 1

Show that if G is a finite group of even order, then G has an odd number of elements of order 2.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:{G}\:\mathrm{is}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{group}\:\mathrm{of} \\ $$$$\mathrm{even}\:\mathrm{order},\:\mathrm{then}\:{G}\:\mathrm{has}\:\mathrm{an}\:\mathrm{odd} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{order}\:\mathrm{2}. \\ $$

Question Number 19634 Answers: 1 Comments: 0

How many ordered triplets (x, y, z) of positive integer satisfy lcm(x, y) = 72, lcm(x, z) = 600 and lcm(y, z) = 900?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{ordered}\:\mathrm{triplets}\:\left({x},\:{y},\:{z}\right)\:\mathrm{of} \\ $$$$\mathrm{positive}\:\mathrm{integer}\:\mathrm{satisfy}\:\mathrm{lcm}\left({x},\:{y}\right)\:=\:\mathrm{72}, \\ $$$$\mathrm{lcm}\left({x},\:{z}\right)\:=\:\mathrm{600}\:\mathrm{and}\:\mathrm{lcm}\left({y},\:{z}\right)\:=\:\mathrm{900}? \\ $$

Question Number 14028 Answers: 0 Comments: 0

Question Number 13200 Answers: 2 Comments: 0

(6)^(1/(5)^(1/(2)^(1/(√3)) ) ) = x How to write x in standard form?

$$\sqrt[{\sqrt[{\sqrt[{\sqrt{\mathrm{3}}}]{\mathrm{2}}}]{\mathrm{5}}}]{\mathrm{6}}\:=\:{x} \\ $$$$\mathrm{How}\:\mathrm{to}\:\mathrm{write}\:{x}\:\mathrm{in}\:\mathrm{standard}\:\mathrm{form}? \\ $$

Question Number 12291 Answers: 1 Comments: 0

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7

Contact: info@tinkutara.com