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Recent questions tagged sets
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1
GATEBOOK2019 Mock Test136
Which of the following statements is/are TRUE? $A \cup (B − C)$ always equals $ (A \cup B) − (A \cup C) $ $A \cap (B − C) $ always equals $(A \cap B) − (A \cap C) $ $A − (B \cap C) $ always equals $(A − B) \cup (A − C) $ $I$ only $I$ and $II$ only $II$ and $III$ only $I, II,$ and $III$
asked
Jan 19
in
Set Theory & Algebra
by
GATEBOOK
Boss
(
15.3k
points)

101
views
gb2019mock1
sets
discretemathematics
0
votes
0
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2
Set Theory
A relation R on a set of positive integers is defined by (a,b) belongs to R iff a and b are relatively prime. Which of the following is true about R? a. Symmetric and Reflexive b. Symmetric and irreflexive c.Symmetric and transitive d. Symmetric and not transitive The Ans is given as (d) but I think (b) is true. Any thoughts?
asked
Nov 8, 2018
in
Set Theory & Algebra
by
dan31
Junior
(
657
points)

59
views
discretemathematics
settheory&algebra
settheory
engineeringmathematics
sets
0
votes
0
answers
3
Rosen
for 3 sets show (AB)C=(AC)(BC) using venn diagrams
asked
Nov 4, 2018
in
Set Theory & Algebra
by
aditi19
Active
(
2.3k
points)

39
views
discretemathematics
kennethrosen
sets
settheory&algebra
venndiagrams
+1
vote
2
answers
4
Set(Problem Related to Subset)
Which of the following is not a subset of $P(P(P(\phi)))$? $A)$ {$\phi$} $B)$ { {$\phi$} } $C)$ { {$\phi$} , { {$\phi$} } } $D)$ { { { {$\phi$} } } }
asked
Oct 5, 2018
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
29k
points)

108
views
discretemathematics
settheory&algebra
sets
+1
vote
0
answers
5
Ace booklet questions no 07
If A∆B = (A intersection B) whole complement than the universal set is??
asked
Sep 18, 2018
in
Set Theory & Algebra
by
Anjali2002
(
17
points)

24
views
acebooklet
settheory&algebra
engineeringmathematics
sets
+1
vote
1
answer
6
Set theory
What will be Cardinality of Cartesian product of a non empty set with a set containing element phi? A={1,2,3} and B={Phi} Than A*B will be 0.
asked
Sep 2, 2018
in
Mathematical Logic
by
Ayan21
(
107
points)

25
views
discretemathematics
settheory&algebra
sets
0
votes
1
answer
7
Relations
What is the smallest binary relation possible from A to B? Is it Null Set? If so, how is it possible relations are subsets of AxB (cartesian product) and if AxB is not supposed to be containing a Null Set.
asked
Aug 22, 2018
in
Set Theory & Algebra
by
superak96
(
177
points)

36
views
sets
relations
discretemathematics
+1
vote
2
answers
8
Doubts
1. What is the Difference Between Range and Co domain of Function ? 2.If i say a function is one to one , onto , bijection what does it actually tell about the function is there any significance or they are just types of function ? 3. when i say ... domain then what's the problem because we can never attain that image because there exist no pre image so how does it effect its range ?
asked
May 30, 2018
in
Mathematical Logic
by
Na462
Loyal
(
8.6k
points)

61
views
engineeringmathematics
discretemathematics
functions
sets
settheory&algebra
0
votes
1
answer
9
Set Theory
How to distinguish between countably finite , countably infinite , uncountably infinite set? for reference see this ques:https://gateoverflow.in/36654/whysetofallfunctionsfn01isuncountablyinfinite
asked
May 15, 2018
in
Set Theory & Algebra
by
srestha
Veteran
(
108k
points)

260
views
discretemathematics
settheory&algebra
settheory
sets
engineeringmathematics
+1
vote
1
answer
10
Proper subset and subset
Please solve this question along with explanation.
asked
May 1, 2018
in
Mathematical Logic
by
saumya mishra
Active
(
1.5k
points)

103
views
sets
+1
vote
1
answer
11
Set system and linear algebra
We have $m$ sets $A_1,A_2,A_3 \text{ to } A_m$. All $A_i \subseteq [n]$ where $ [n] = \{1,2,3, \dots n \}.$ Given that $A_i = \text{odd number}$ and $A_i \cap A_j = \text{even number }\forall i \neq j$. Show that $m \leq n$.
asked
Apr 16, 2018
in
Set Theory & Algebra
by
Debashish Deka
Veteran
(
58k
points)

392
views
sets
linearalgebra
combinatoricsiitb
0
votes
1
answer
12
Group theory
Let $G$ be a finite group with sub group $H$ & $K$ such that $H=7$ and $K=31$ then find $ H ⋂ K$
asked
Mar 6, 2018
in
Set Theory & Algebra
by
Deepesh Pai
(
499
points)

90
views
engineeringmathematics
settheory&algebra
sets
+1
vote
2
answers
13
UGC NET DEC 2012 PAPER II Q4
4. The power set of the set {ϕ} is (A) {ϕ} (B) {ϕ, {ϕ}} (C) {0} (D) {0, ϕ, {ϕ}}
asked
Feb 5, 2018
in
Set Theory & Algebra
by
kavikeve
(
493
points)

271
views
ugcnetdec2012ii
settheory&algebra
sets
+2
votes
1
answer
14
Set theory
Let $f: A \to B$ be a function and $S$ and $T$ be subsets of $B$. Consider the following statements about image (range) : $S1:\quad f^{1}(S \cup T) = f^{1}(S) \cup f^{1}(T)$ $S2:\quad f^{1}(S \cap T) = f^{1}(S) \cap f^{1}(T)$ Which of the following is correct? A) only S1 is true B) only S2 is true C) Both S1 and S2 is true D) Neither S1 nor S2 is true
asked
Dec 31, 2017
in
Set Theory & Algebra
by
ashish pal
Active
(
1.2k
points)

123
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discretemathematics
settheory&algebra
sets
engineeringmathematics
settheory
+3
votes
1
answer
15
Power Set
$R=P\left ( P\left ( P\left ( \phi \right ) \right ) \right )$ $T=P\left ( P\left ( \left \{ 1,2 \right \} \right ) \right )$ What is cardinality of set $S$, where $S=R\times T$
asked
Dec 28, 2017
in
Set Theory & Algebra
by
srestha
Veteran
(
108k
points)

87
views
discretemathematics
sets
0
votes
0
answers
16
Most efficient data structure to implement Sets of Integer and what is the complexity of operation......
asked
Oct 27, 2017
in
DS
by
Rohit Gupta 8
Active
(
2.2k
points)

117
views
algorithms
datastructure
sets
+1
vote
3
answers
17
Set theory doubt
Say if A is proper subset of B i.e A⊂B then is it true  that B⊆A (B is subset of A)? Also one more thing  if A⊂B then AUB = A where U means UNION
asked
Sep 5, 2017
in
Set Theory & Algebra
by
iarnav
Loyal
(
9.5k
points)

159
views
discretemathematics
settheory&algebra
sets
settheory
+1
vote
1
answer
18
Discrete Maths Kenneth H. Rosen Ex 9.4 Relations
Hi, following is a question from Kenneth H. Rosen : Find the smallest relation containing the relation R ={(a, b)  a>b} that is both reﬂexive and symmetric? The online solution given to the above problem is : ... the closure(which should be reflexive and symmetric) of the given relation? Can someone please help me understand this question?
asked
Aug 2, 2017
in
Set Theory & Algebra
by
Piyush Agarwal
(
33
points)

185
views
kennethrosen
discretemathematics
settheory&algebra
sets
+1
vote
1
answer
19
Rosen 2.5.22
Suppose that A is a countable set. Show that the set B is also countable if there is an onto function f from A to B.
asked
Jul 29, 2017
in
Set Theory & Algebra
by
sarika
(
217
points)

109
views
sets
kennethrosen
+1
vote
1
answer
20
Set Theory Doubt
Want to verify let set $\left  A \right =n$ and $\left  B \right =m$ Then $max(m,n)\leq \left  A\cup B \right \leq (m+n)$ $0\leq \left  A\cap B \right \leq min(m,n)$ $0\leq \left  A B \right \leq \left  n \right $ ... $\bigoplus$ is symmetric difference $0\leq \left  \overline{A} \right \leq U$ here $\overline{A}$ is compliment of A and U is universal Set
asked
Jul 25, 2017
in
Set Theory & Algebra
by
Tesla!
Boss
(
17.8k
points)

138
views
discretemathematics
settheory&algebra
sets
+2
votes
1
answer
21
Set theory
{ a } ∈ A but a ∉ A why ? here ' a is the element of set {a} ' ,and ' set {a} is the element of A" , so " a also element of A " . please clear my doubt .
asked
Jun 16, 2017
in
Set Theory & Algebra
by
ram_18051996
(
379
points)

135
views
settheory&algebra
discretemathematics
engineeringmathematics
sets
+1
vote
2
answers
22
ISRO201777
If $L$ and $P$ are two recursively enumerable languages then they are not closed under Kleene star $L^*$ of $L$ Intersection $L \cap P$ Union $L \cup P$ Set difference
asked
May 7, 2017
in
Theory of Computation
by
sh!va
Boss
(
35.2k
points)

2.9k
views
isro2017
sets
theoryofcomputation
recursiveandrecursivelyenumerablelanguages
closureproperty
badquestion
+7
votes
5
answers
23
ISRO20179
The symmetric difference of sets $A=\{1,2, 3,4, 5, 6, 7, 8\}$ and $B= \{1, 3, 5, 6, 7,8,9\}$ is: $\{1, 3, 5, 6, 7,8\}$ $\{2, 4, 9\}$ $\{2, 4\}$ $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$
asked
May 7, 2017
in
Set Theory & Algebra
by
sh!va
Boss
(
35.2k
points)

3k
views
isro2017
settheory&algebra
sets
+2
votes
1
answer
24
Discrete Mathematics Thegatebook
If $A=\phi$ then $A\times B =\phi?$ I mean $A$ is a null set or empty set
asked
May 5, 2017
in
Set Theory & Algebra
by
Lakshman Patel RJIT
Boss
(
29k
points)

405
views
discretemathematics
settheory&algebra
sets
0
votes
1
answer
25
No of one to one function
No of one to one function from set A={1,2,3,4,5,6,7,8,9} to set B ={x1,x2,x3,x4,x5,x6,x7,.....,xn}
asked
May 2, 2017
in
Linear Algebra
by
ashwina
Active
(
2.1k
points)

232
views
engineeringmathematics
sets
iiithpgee
0
votes
1
answer
26
Set theory
Justify your answer with valid reason $\phi \epsilon \left \{ A \right \} \wedge \phi \subseteq \left \{ A \right \}$ Where A is an non empty set $\left  A \right  \neq 0$
asked
Apr 2, 2017
in
Algorithms
by
Tesla!
Boss
(
17.8k
points)

87
views
settheory&algebra
discretemathematics
sets
0
votes
1
answer
27
Set theory
Let S be a set of n elements and let p(S) be its power set. Then find total number of ordered pairs such that $s1 \cap s2 = \phi$ where s1 & s2 are subset of p(s)
asked
Apr 2, 2017
in
Algorithms
by
Tesla!
Boss
(
17.8k
points)

135
views
settheory&algebra
discretemathematics
sets
permutationsandcombinations
+1
vote
2
answers
28
group theory
"the union of two subgroups neednot be a subgroup".can somebody prove without using counter example ...
asked
Mar 25, 2017
in
Set Theory & Algebra
by
Vicky rix
Loyal
(
8.1k
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143
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discretemathematics
groups
settheory&algebra
engineeringmathematics
sets
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