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Recent questions and answers in Set Theory & Algebra
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1
Kenneth Rosen Edition 7th Exercise 2.2 Question 32 (Page No. 137)
Find the symmetric difference of $\left \{ 1,3,5 \right \}$ and $\left \{ 1,2,3 \right \}.$
answered
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Set Theory & Algebra
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Kenneth Rosen Edition 7th Exercise 2.2 Question 35 (Page No. 137)
Show that $A\oplus B = (A \cup B) – (A \cap B).$
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Set Theory & Algebra
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Lakshman Patel RJIT
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Kenneth Rosen Edition 7th Exercise 2.2 Question 36 (Page No. 137)
Show that $A \oplus B = (AB) \cup (BA).$
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Set Theory & Algebra
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Kenneth Rosen Edition 7th Exercise 2.2 Question 37 (Page No. 137)
Show that if $A$ is a subset of a universal set $U$, then $A \oplus A = \phi.$ $A \oplus \phi = A.$ $A \oplus U = \sim A.$ $A \oplus \sim A= U.$
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Set Theory & Algebra
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Kenneth Rosen Edition 7th Exercise 2.3 Question 69 (Page No. 155)
Find the inverse function of $f(x) = x^3 +1.$
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Set Theory & Algebra
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6
UGCNETJune2019II1
Consider the poset $( \{3,5,9,15,24,45 \}, )$ Which of the following is correct for the given poset ? There exist a greatest element and a least element There exist a greatest element but not a least element There exist a least element but not a greatest element There does not exist a greatest element and a least element
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Jul 8
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poset
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7
Kenneth Rosen Edition 6th Exercise 7.5 Question 3 e (Page No. 507)
Which of these relations on the set of all functions from Z to Z are equivalence relations? Determine the properties of an equivalence relation that the others lack. {(f, g)  f(0) = g(1) and f(1) = g(0)} In many ... made to check the reflexive property. Why can't we check f(0)=f(0) to confirm the reflexive property. Please help.
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Jul 5
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srestha
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112k
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8
UGCNETJune2019II13
answered
Jul 3
in
Set Theory & Algebra
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Satbir
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ugcnetjune2019ii
boolean
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9
UGCNETJune2019II9
Find the zeroone matrix of the transitive closure of the relation given by the matrix $A$ : $A =\begin{bmatrix} 1 & 0& 1\\ 0 & 1 & 0\\ 1& 1& 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 1& 1\\ 0 & 1 & 0\\ 1& 0& 1 \end{bmatrix}$
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Jul 3
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Set Theory & Algebra
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Ram Swaroop
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ugcnetjune2019ii
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10
Kenneth Rosen Edition 7th Exercise 2.1 Question 23 (Page No. 126)
How many elements does each of these sets have where $a$ and $b$ are distinct elements? $P (\left \{a,b, \left \{a,b \right \} \right \})$ $P\left \{ \phi, a, \left \{ a \right \},\left \{ \left \{ a \right \} \right \}\right \}$ $P(P(\phi ))$
answered
Jul 1
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Set Theory & Algebra
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srestha
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kennethrosen
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0
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11
Kenneth Rosen Edition 7th Exercise 2.1 Question 24 (Page No. 126)
Determine whether each of these sets is the power set of a set, where $a$ and $b$ are distinct elements. $\phi$ $\left \{ \phi ,\left \{ a \right \} \right \}$ $\left \{ \phi ,\left \{ a \right \},\left \{ \phi ,a \right \} \right \}$ $\left \{ \phi ,\left \{ a \right \},\left \{ b \right \},\left \{ a,b \right \} \right \}$
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Jul 1
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Set Theory & Algebra
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srestha
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19
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kennethrosen
discretemathematics
settheory&algebra
+18
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5
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12
GATE20022.17
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetric Symmetric and reflexive Transitive and reflexive Transitive and symmetric
answered
Jun 23
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Set Theory & Algebra
by
pritishc
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81
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gate2002
settheory&algebra
normal
relations
+9
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3
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13
GATE19982.4
In a room containing $28$ people, there are $18$ people who speak English, $15$, people who speak Hindi and $22$ people who speak Kannada. $9$ persons speak both English and Hindi, $11$ persons speak both Hindi and Kannada whereas $13$ persons speak both Kannada and English. How many speak all three languages? $9$ $8$ $7$ $6$
answered
Jun 18
in
Set Theory & Algebra
by
Nithin2698
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27
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gate1998
settheory&algebra
easy
sets
+10
votes
4
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14
GATE19891iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
answered
Jun 18
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Set Theory & Algebra
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mohan123
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gate1989
settheory&algebra
relations
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+2
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1
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15
GATE19994
Let $G$ be a finite group and $H$ be a subgroup of $G$. For $a \in G$, define $aH=\left\{ah \mid h \in H\right\}$. Show that $aH = bH.$ Show that for every pair of elements $a, b \in G$, either $aH = bH$ or $aH$ and $bH$ are disjoint. Use the above to argue that the order of $H$ must divide the order of $G.$
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Jun 16
in
Set Theory & Algebra
by
Satbir
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15.3k
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485
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gate1999
settheory&algebra
groups
normal
cosets
+8
votes
3
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16
TIFR2011B23
Suppose $(S_{1}, S_{2},\ldots,S_{m})$ is a finite collection of nonempty subsets of a universe $U.$ Note that the sets in this collection need not be distinct. Consider the following basic step to be performed on this sequence. While there exist sets $S_{i}$ and ... of a finite universe $U$ and a choice of $S_{i}$ and $S_{j}$ in each step such that the process does not terminate.
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Jun 16
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Set Theory & Algebra
by
Arjun
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413k
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360
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tifr2011
settheory&algebra
sets
+16
votes
3
answers
17
GATE199811
Suppose $A = \{a, b, c, d\}$ and $\Pi_1$ is the following partition of A $\Pi_1 = \left\{\left\{a, b, c\right\}\left\{d\right\}\right\}$ List the ordered pairs of the equivalence relations induced by $\Pi_1$. Draw the graph of the above equivalence relation ... $\left\langle\left\{\Pi_1, \Pi_2, \Pi_3, \Pi_4\right\}, \text{ refines } \right\rangle$.
answered
Jun 15
in
Set Theory & Algebra
by
Satbir
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15.3k
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1.6k
views
gate1998
settheory&algebra
normal
partialorder
descriptive
+7
votes
1
answer
18
TIFR2018B10
For two $n$ bit strings $x,y \in\{0,1\}^{n},$ define $z=x\oplus y$ to be the bitwise XOR of the two strings (that is, if $x_{i},y_{i},z_{i}$ denote the $i^{th}$ bits of $x,y,z$ respectively, then $z_{i}=x_{i}+y_{i} \bmod 2$ ... The number of such linear functions for $n \geq 2$ is: $2^{n}$ $2^{n^{2}}$ $\large2^{\frac{n}{2}}$ $2^{4n}$ $2^{n^{2}+n}$
answered
Jun 14
in
Set Theory & Algebra
by
Arjun
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413k
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230
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tifr2018
functions
+1
vote
2
answers
19
GATE199017c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
answered
Jun 8
in
Set Theory & Algebra
by
Arjun
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413k
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243
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gate1990
descriptive
settheory&algebra
lattice
+7
votes
1
answer
20
GATE19879e
How many true inclusion relations are there of the from $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
answered
Jun 7
in
Set Theory & Algebra
by
Arjun
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413k
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448
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gate1987
settheory&algebra
relations
0
votes
1
answer
21
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
answered
Jun 6
in
Set Theory & Algebra
by
Arjun
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413k
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107
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gate1995
settheory&algebra
numericalanswers
sets
0
votes
0
answers
22
Doubt on a math question
Chk this question https://gateoverflow.in/100202/testseriescounting $1)$Can someone verify this ans?? See if $\left ( _{0}^{6}\textrm{C} \right )$ in one set, other set will contain $\left ( _{6}^{6}\textrm{C} \right )$ elements. right?? Now why do we again need $2^{n}$ ... meaning of it?? $2)$ How $\sum_{I=0}^{n}\left ( _{i}^{n}\textrm{C} \right ).2^{ni}=3^{n}$??
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Jun 4
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Set Theory & Algebra
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srestha
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112k
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24
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discretemathematics
settheory&algebra
0
votes
0
answers
23
Ace booklet functions page:152 q.no 44
Let A, B, C are k element sets and let S be an n element set where k<=n. How many triples of functions f:A>S, g:B>S, h:C>S are there such that f, g and h are all injective and f(A) =g(B) =h(C) =?
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May 27
in
Set Theory & Algebra
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chandan2teja
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127
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20
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0
votes
0
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24
Ace workbook lattice concept
If X is minimum element of S then X is related to y for all y belongs to S. Let [S;R] be a poset. If every non empty subset of S has a minimum element then a) S is Totally ordered set b) S is bounded set. C) S is complemented ... then 1 will be part of every non empty subset of S. Is this correct way of interpreting the question. If not can you please elaborate it
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May 26
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Set Theory & Algebra
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127
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20
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0
votes
0
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25
Hasse Doubt
what is the least upper bound of {a, b, c}?
asked
May 23
in
Set Theory & Algebra
by
aditi19
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57
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hassediagram
settheory&algebra
lattice
partialorder
+2
votes
1
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26
CMI2011B02a
Let $G$ be a connected graph. For a vertex $x$ of $G$ we denote by $G−x$ the graph formed by removing $x$ and all edges incident on $x$ from $G$. $G$ is said to be good if there are at least two distinct vertices $x, y$ in $G$ such that both $G − x$ and $G − y$ are connected. Show that for any subgraph $H$ of $G$, $H$ is good if and only if $G$ is good.
answered
May 21
in
Set Theory & Algebra
by
Kushagra Chatterjee
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9.5k
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cmi2011
descriptive
graphconnectivity
proof
0
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1
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27
Made Easy Test Series:Lattice
The number of totally ordered set compatible to the given POSET are __________
answered
May 20
in
Set Theory & Algebra
by
Satbir
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15.3k
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55
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madeeasytestseries
lattice
0
votes
1
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28
ISI2018MMA15
Let $G$ be a finite group of even order. Then which of the following statements is correct? The number of elements of order $2$ in $G$ is even The number of elements of order $2$ in $G$ is odd $G$ has no subgroup of order $2$ None of the above.
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May 20
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Set Theory & Algebra
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Harsh Kumar
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33
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isi2018
engineeringmathematics
discretemathematics
settheory&algebra
groups
0
votes
1
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29
Discrete mathematics #TEST_BOOK
I Have doubt about the language. Is it asking about the sum of elements if we make the GBL set for the given lattice .
answered
May 20
in
Set Theory & Algebra
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Arkaprava
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#discrete
#lattice
0
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30
Made Easy Test Series:Discrete MathematicsPoset
Consider the following Posets: $I)\left ( \left \{ 1,2,5,7,10,14,35,70 \right \},\leq \right )$ $II)\left ( \left \{ 1,2,3,6,14,21,42 \right \},/ \right )$ $III)\left ( \left \{ 1,2,3,6,11,22,33,66 \right \},/ \right )$ Which of the above poset are isomorphic to $\left ( P\left ( S \right ),\subseteq \right )$ where $S=\left \{ a,b,c \right \}?$
answered
May 18
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Set Theory & Algebra
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Hirak
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poset
madeeasytestseries
discretemathematics
0
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31
Discrete Mathematics by Kenneth Rosen,section2.4,recursive functions
$C_{a}^{k}:\mathbb{N}^{k}\rightarrow \mathbb{N}$ I am studying discrete math from beginnings and came across this term in primitive recursive function.I don't know what $C_{a}^{k}$ means and does $\mathbb{N}$ means set of natural numbers?Someone please help me out.
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May 15
in
Set Theory & Algebra
by
souren
(
37
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38
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discretemathematics
settheory&algebra
kennethrosen
0
votes
1
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32
ISI2018PCBB3
An $n$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ denote the number of such functions. Calculate the value of $\sigma_4$. Derive an expression for $\sigma_n$ in terms of $n$.
answered
May 12
in
Set Theory & Algebra
by
Arkaprava
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18
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isi2018pcbb
engineeringmathematics
discretemathematics
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functions
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0
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1
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33
ISI2018PCBA4
Let $A$ and $B$ are two nonempty finite subsets of $\mathbb{Z}$, the set of all integers. Define $A+B=\{a+b:a\in A,b\in B\}$.Prove that $A+B\geq A +B 1 $, where $S$ denotes the cardinality of finite set $S$.
answered
May 12
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Set Theory & Algebra
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Arkaprava
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23
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isi2018pcba
engineeringmathematics
discretemathematics
settheory&algebra
descriptive
+2
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4
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34
GATE 2019
Let U = {1, 2, ..., n} and A = {(x, X), x ∈ X and X ⊆ U}. Consider the following two statements for A. (i) A = n*$\small 2^{n1}$ (ii) A= Sigma(k=1 to n) k.(nCk) Which of the following is correct? (a) (i) only (b) (ii) only (c) Both (i) and (ii) (d) None of the above
answered
May 11
in
Set Theory & Algebra
by
Umakant_Mukhiya
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29
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718
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0
votes
0
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35
Rosen 7e Exercise9.6 Question no27 page no631
What is the covering relation of the partial ordering {(A, B)  A ⊆ B} on the power set of S, where S = {a, b, c}? i'm getting R={(Ф, {a}), (Ф, {b}), (Ф, {c}), (Ф, {a, b}), (Ф, {b, c}), (Ф, {a, c}), (Ф, {a, b, c}), ({a}, {a, b}), ({a}, {a, c}), ({b}, ... b, c}), ({c}, {a, c}), ({c}, {b, c}), ({a, b}, {a, b, c}), ({a, c}, {a, b, c})({b, c}, {a, b, c})
asked
May 10
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Set Theory & Algebra
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aditi19
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50
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kennethrosen
discretemathematics
relations
settheory&algebra
settheory
sets
+1
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0
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36
Which Statement is correct for the given sets statements
If A, B, C are three sets then which of the following is TRUE ? If ( A ∩ C ) = ( B ∩ C ) then A = B If ( A ∪ C ) = ( B ∪ C ) then A = B If ( A 𝜟 C ) = ( B 𝜟 C ) then A = B If ( A – C ) = ( B – C ) then A = B
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May 10
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Set Theory & Algebra
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pranay91331
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49
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42
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settheory&algebra
sets
discretemathematics
0
votes
1
answer
37
Kenneth Rosen Edition 7th Exercise 2.3 Question 72 (Page No. 155)
Suppose that $f$ is a function from $A$ to $B$, where $A$ and $B$ are finite sets with $A=B$. Show that $f$ is onetoone if and only if it is onto.
answered
May 8
in
Set Theory & Algebra
by
Arkaprava
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2.1k
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34
views
kennethrosen
discretemathematics
settheory&algebra
+1
vote
1
answer
38
ISI2019MMA19
Let $G =\{a_1,a_2, \dots ,a_{12}\}$ be an Abelian group of order $12$ . Then the order of the element $ ( \prod_{i=1}^{12} a_i)$ is $1$ $2$ $6$ $12$
answered
May 8
in
Set Theory & Algebra
by
Shikha Mallick
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3.4k
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189
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isi2019
engineeringmathematics
discretemathematics
settheory&algebra
groups
+16
votes
4
answers
39
GATE199317
Out of a group of $21$ persons, $9$ eat vegetables, $10$ eat fish and $7$ eat eggs. $5$ persons eat all three. How many persons eat at least two out of the three dishes?
answered
May 5
in
Set Theory & Algebra
by
manohar
Junior
(
535
points)

1.7k
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gate1993
settheory&algebra
easy
sets
descriptive
0
votes
1
answer
40
IIT Madras MS written test 2019
Which of the following infinite sets have the same cardinality? $\mathbb{N}$ : Set of Natural numbers $\mathbb{E}$ : Set of Even numbers $\mathbb{Q}$ : Set of Rational numbers $\mathbb{R}$ : Set of Real numbers $\mathbb{N}$ and $\mathbb{E}$ $\mathbb{Q}$ and $\mathbb{R}$ $\mathbb{R}$ and $\mathbb{N}$ None of the above
answered
May 2
in
Set Theory & Algebra
by
royal shubham
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727
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82
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iitmadras
ms
writtentest
2019
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