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Set TheoryQuestion and Answers: Page 6

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

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

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.

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

Question Number 22162 Answers: 1 Comments: 0

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

$u s e t h e a p p r o p i t e s e t l a w t o s h o w$ $t h a t$ $(A - B) \cup (B - A) = (A \cup B) - (A \cap B)$

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

$T h e s t u d e n t s w e r e a s k e d w h e t h e r$ $t h e y h a d d i c t i o n a r y (D) o r t h e s a u$ $r u s (T) i n t h e i r r o o m . t h e r e s u l t s$ $s h o w e d t h a t 650 s t u d e n t s h a d d i c t$ $i o n a r y, 150 d i d n o t h a d d i c t i o n a r y,$ $175 h a d a t h e s a u r u s, a n d 50 h a d$ $n e i t h e r a d i c t i o n a r y n o r a t h e s a u r$ $u s, f i m d t h e n u m b e r o f s t u d e n t w h o$ $(i) l i v e i n d o m i t o r y$ $(i i) h a v e b o t h d i c t i o n a r y a n d t h e s a u r u s$ $(i i i) h a v e o n l y t h e s a u r u s$

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.

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

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?

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

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?

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

Question Number 12291 Answers: 1 Comments: 0

Question Number 10000 Answers: 0 Comments: 0

An analyst was hired to survey 20 students. He reported that 6 eat eba, 5 eat amala and 7 eat semovita. 9 eat eba or amala, 12 amala or semovita and 9 eba or semovita. 3 eat all the three food and 10 eat none. After a careful analysis of these findings, the analyst was fired. why ???

$An analyst was hired to survey 20 students .$ $He reported that 6 eat eba, 5 eat amala and$ $7 eat semovita . 9 eat eba or amala, 12 amala$ $or semovita and 9 eba or semovita . 3 eat all$ $the three food and 10 eat none . After a careful$ $analysis of these findings, the analyst was fired .$ $why ? ? ?$

Question Number 9423 Answers: 1 Comments: 3

if x and y are two sets such that n(x) =17 , n(y)=23 and n(X∪Y) =38, find n(X∪Y).

$i f x a n d y a r e t w o s e t s s u c h t h a t n (x)$ $= 17, n (y) = 23 a n d n (X \cup Y) = 38,$ $f i n d n (X \cup Y) .$

Question Number 7440 Answers: 0 Comments: 7

Prove that If A, B and C are subset of the same universal set then (A − B) ∩ (A − C) = A − (B − C)

$P r o v e t h a t$ $I f A, B a n d C a r e s u b s e t o f t h e s a m e u n i v e r s a l s e t$ $t h e n (A - B) \cap (A - C) = A - (B - C)$

Question Number 5446 Answers: 2 Comments: 0

$7$

Question Number 5088 Answers: 0 Comments: 0

According to wikipedia, the cardonality of a set of all finite subsets of any countably infinite set is ℵ_0 . How can we prove this?

$According to wikipedia,$ $the cardonality of a set of all f i n i t e$ $subsets of any countably infinite set$ $is ℵ_{0} .$ $How can we prove this ?$

Question Number 5080 Answers: 0 Comments: 0

N = {0, 1, 2, ...} ∣N∣ = ℵ_0 I know that: if S = {k, 0, 1, 2, ...} ∴ ∣S∣ = ∣N∣ = ℵ_0 Because you can forever pair one value from one set to another. In my question bellow I use the word ′combine′. What I mean is something like this: {1, 2, 3} + {2, 3, 4} = {1, 2, 3, 2, 3, 4} or = {1, 2, 2, 3, 3, 4} order doesn′t matter i am unsure how to write this mathematically correct My question is as follows: If we combine ℵ_0 lots of sets, with each set containing ℵ_0 values, is the total values greater than ℵ_0 ? e.g. G = N + N + ... + N ℵ_0 times G = {0, 0, ..., 1, 1, ..., 2, 2, ...} Is ∣G∣>ℵ_0 ?

$N = {0, 1, 2, . . .}$ $∣ N ∣ = ℵ_{0}$ $I know that :$ $if S = {k, 0, 1, 2, . . .}$ $∴ ∣ S ∣ = ∣ N ∣ = ℵ_{0}$ $Because you can forever pair one value$ $from one set to another .$ $In my question bellow I use the word$ $^{'} {c o m b i n e}^{'} . What I mean is something$ $like this :$ ${1, 2, 3} + {2, 3, 4} = {1, 2, 3, 2, 3, 4}$ $o r = {1, 2, 2, 3, 3, 4}$ $o r d e r {d o e s n}^{'} t m a t t e r$ $i a m u n s u r e h o w t o w r i t e t h i s m a t h e m a t i c a l l y c o r r e c t$ $My question is as follows :$ $If we combine ℵ_{0} lots of sets, with each$ $set containing ℵ_{0} values, is the total$ $values greater than ℵ_{0} ?$ $e . g .$ $G = N + N + . . . + N ℵ_{0} times$ $G = {0, 0, . . ., 1, 1, . . ., 2, 2, . . .}$ $Is ∣ G ∣> ℵ_{0} ?$

Question Number 4733 Answers: 0 Comments: 10

Question Number 4027 Answers: 0 Comments: 2

Let A denotes the Set of Algebraic Numbers and T the Set of Trancedental Numbers. Discuss the following: •Are A and T closed with respect to addition and multiplication ? •Are A−{0) and T closed with respect to division?

$L e t A d e n o t e s t h e S e t o f A l g e b r a i c N u m b e r s$ $a n d T t h e S e t o f T r a n c e d e n t a l N u m b e r s .$ $D i s c u s s t h e f o l l o w i n g :$ $∙ A r e A a n d T c l o s e d w i t h r e s p e c t t o$ $a d d i t i o n a n d m u l t i p l i c a t i o n ?$ $∙ A r e A - {0) a n d T c l o s e d w i t h r e s p e c t t o$ $d i v i s i o n ?$

Question Number 3551 Answers: 0 Comments: 4

Prove that P set of prime numbers is countable.

$Prove that P set of prime numbers is$ $countable .$

Question Number 3130 Answers: 2 Comments: 0

If A,B,C and D are any four sets then (i) (A−B)∪(C−D)=^(?) (A∪C)−(B∪D) (ii) (A−B)∪(C−D)=^(?) (A∪C)−(B∩D)

$I f A, B, C a n d D a r e a n y f o u r s e t s t h e n$ $(i) (A - B) \cup (C - D) \overset{?}{=} (A \cup C) - (B \cup D)$ $(i i) (A - B) \cup (C - D) \overset{?}{=} (A \cup C) - (B \cap D)$

Question Number 1875 Answers: 0 Comments: 0

Given that: Z={0, 1, 2, ...} all integers ≥0 R={0, 0.01, ..., 1, 1.01, ...} all reals ≥0 Prove that ∣R∣>∣Z∣

$Given that :$ $Z = {0, 1, 2, . . .} all integers ⩾ 0$ $R = {0, 0.01, . . ., 1, 1.01, . . .} all reals ⩾ 0$ $Prove that ∣ R ∣>∣ Z ∣$

Question Number 1763 Answers: 1 Comments: 1

Question Number 1744 Answers: 3 Comments: 0

If A and B are two sets and U is a universal set prove that A ⊆ B ⇒ B=A ∪ (A′ ∩ B)

$I f A a n d B a r e t w o s e t s a n d U i s$ $a u n i v e r s a l s e t p r o v e t h a t$ $A \subseteq B \Rightarrow B = A \cup (A^{'} \cap B)$

Question Number 1698 Answers: 2 Comments: 0

•Are A∪B=A∩B and A=B completely equivalent? •Simplify A∪B=A∩B to A=B using set operations and their properties.

$∙ A r e A \cup B = A \cap B a n d A = B$ $c o m p l e t e l y e q u i v a l e n t ?$ $∙ S i m p l i f y A \cup B = A \cap B t o A = B$ $u s i n g s e t o p e r a t i o n s a n d t h e i r$ $p r o p e r t i e s .$

Question Number 1694 Answers: 2 Comments: 0

proof that for two set A and B (or give a counter example) ∣A∪B∣≥∣A∩B∣

$proof that for two set A and B (or give a counter example)$ $∣ A \cup B ∣⩾∣ A \cap B ∣$

Question Number 1682 Answers: 0 Comments: 5

Let ∣ S ∣ denotes number of elements in a set S , N and R are sets of natural and real numbers respectively: ∣ N ∣=^(?) ∣ R ∣

$L e t ∣ S ∣ d e n o t e s n u m b e r o f e l e m e n t s i n a s e t S,$ $N a n d R a r e s e t s o f n a t u r a l a n d r e a l n u m b e r s$ $r e s p e c t i v e l y :$ $∣ N ∣ \overset{?}{=} ∣ R ∣$

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

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