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Recent questions tagged set-theory&algebra
4
votes
2
answers
821
views
GATE CSE 2021 Set 2 | Question: 11 | Video Solution
Arjun
asked
in
Set Theory & Algebra
Feb 18, 2021
by
Arjun
1.4k
points
821
views
gate2021-cse-set2
multiple-selects
set-theory&algebra
functions
1
vote
1
answer
490
views
GATE CSE 2021 Set 2 | Question: 37 | Video Solution
Arjun
asked
in
Set Theory & Algebra
Feb 18, 2021
by
Arjun
1.4k
points
490
views
gate2021-cse-set2
set-theory&algebra
sets
3
votes
2
answers
627
views
GATE CSE 2021 Set 1 | Question: 34 | Video Solution
Arjun
asked
in
Set Theory & Algebra
Feb 18, 2021
by
Arjun
1.4k
points
627
views
gate2021-cse-set1
set-theory&algebra
group-theory
3
votes
4
answers
767
views
GATE CSE 2021 Set 1 | Question: 43 | Video Solution
Arjun
asked
in
Set Theory & Algebra
Feb 18, 2021
by
Arjun
1.4k
points
767
views
gate2021-cse-set1
multiple-selects
set-theory&algebra
relations
1
vote
1
answer
113
views
LATTICE ASSOCIATIVITY DOUBT
I wasn't convinced about the associativity property of lattices, and the proof i found on math.stackexchange seemed reasonable, but still i couldnt wrap my head around it. I tried to make a counter example, and in the above diagram (b join c) ... otherwise it would've satisfied associativity. But i cant seem to figure out why this diagram isn't a lattice. Please help.
rish-18
asked
in
Set Theory & Algebra
Aug 22, 2020
by
rish-18
13
points
113
views
discrete-mathematics
set-theory&algebra
self-doubt
0
votes
0
answers
28
views
GATE2015-1-39 Video Solution
Consider the operations $\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}$ and $\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}$ Which one of the following is correct? Both $\left\{\textit{f} \right\}$ and $\left\{ \textit{g}\right\}$ ... $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
28
views
gate2015-1
set-theory&algebra
functions
difficult
video-solution
0
votes
0
answers
22
views
GATE1997-6.3 Video Solution
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
22
views
gate1997
set-theory&algebra
relations
normal
video-solution
0
votes
0
answers
16
views
GATE2015-2-40 Video Solution
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
16
views
gate2015-2
set-theory&algebra
functions
normal
numerical-answers
video-solution
0
votes
0
answers
35
views
GATE2016-1-28 Video Solution
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$,satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
35
views
gate2016-1
set-theory&algebra
functions
normal
numerical-answers
video-solution
0
votes
0
answers
17
views
GATE2005-7 Video Solution
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
17
views
gate2005
set-theory&algebra
normal
relations
video-solution
0
votes
0
answers
31
views
GATE2018-27 Video Solution
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
31
views
gate2018
set-theory&algebra
countable-uncountable-set
normal
video-solution
0
votes
0
answers
48
views
GATE2015-1-34 Video Solution
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram: For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \wedge y$ are join and meet of $x, y$ ... $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
48
views
gate2015-1
set-theory&algebra
normal
lattice
video-solution
0
votes
0
answers
15
views
GATE2015-1-16 Video Solution
For a set $A$, the power set of $A$ is denoted by $2^{A}$. If $A = \left\{5,\left\{6\right\}, \left\{7\right\}\right\}$, which of the following options are TRUE? $\phi \in 2^{A}$ $\phi \subseteq 2^{A}$ $\left\{5,\left\{6\right\}\right\} \in 2^{A}$ $\left\{5,\left\{6\right\}\right\} \subseteq 2^{A}$ I and III only II and III only I, II and III only I, II and IV only
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
15
views
gate2015-1
set-theory&algebra
sets
normal
video-solution
0
votes
0
answers
60
views
GATE2016-2-28 Video Solution
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an ... \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
60
views
gate2016-2
set-theory&algebra
difficult
sets
video-solution
0
votes
0
answers
21
views
GATE2014-3-50 Video Solution
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
21
views
gate2014-3
set-theory&algebra
group-theory
numerical-answers
normal
video-solution
0
votes
0
answers
18
views
GATE2014-3-49 Video Solution
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$. For each such function it must be the case that for every ... is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
18
views
gate2014-3
set-theory&algebra
functions
normal
video-solution
0
votes
0
answers
23
views
GATE2014-2-50 Video Solution
Consider the following relation on subsets of the set $S$ of integers between 1 and 2014. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the following two ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
23
views
gate2014-2
set-theory&algebra
normal
sets
video-solution
0
votes
0
answers
21
views
GATE2016-2-26 Video Solution
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
21
views
gate2016-2
set-theory&algebra
relations
normal
video-solution
0
votes
0
answers
25
views
GATE2005-44 Video Solution
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
admin
asked
in
Combinatory
Apr 18, 2020
by
admin
585
points
25
views
gate2005
set-theory&algebra
normal
pigeonhole-principle
video-solution
0
votes
0
answers
19
views
GATE2017-2-24 Video Solution
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
19
views
gate2017-2
polynomials
numerical-answers
set-theory&algebra
video-solution
0
votes
0
answers
19
views
GATE2014-3-2 Video Solution
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE? For any subsets $A$ and $B$ of $X, |fA \cup B| = |f(A)| + |f(B)|$ For any subsets $A$ and $B$ of $X, f(A \cap B) = f(A) \cap f(B)$ For any subsets $A$ ... $S$ and $T$ of $Y, f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
19
views
gate2014-3
set-theory&algebra
functions
normal
video-solution
0
votes
0
answers
21
views
GATE2014-1-50 Video Solution
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
21
views
gate2014-1
set-theory&algebra
functions
combinatory
numerical-answers
video-solution
0
votes
0
answers
20
views
GATE2000-2.6 Video Solution
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
20
views
gate2000
set-theory&algebra
easy
sets
video-solution
0
votes
0
answers
36
views
GATE2019-10 Video Solution
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
36
views
gate2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
video-solution
0
votes
0
answers
20
views
GATE2018-19 Video Solution
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
20
views
gate2018
group-theory
numerical-answers
set-theory&algebra
video-solution
0
votes
0
answers
17
views
GATE2017-2-21 Video Solution
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
17
views
gate2017-2
set-theory&algebra
lattice
numerical-answers
normal
video-solution
0
votes
0
answers
21
views
GATE2015-3-41 Video Solution
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about R? Both reflexive and symmetric Reflexive but not symmetric Not reflexive but symmetric Neither reflexive nor symmetric
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
21
views
gate2015-3
set-theory&algebra
relations
normal
video-solution
0
votes
0
answers
19
views
GATE2007-26 Video Solution
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
19
views
gate2007
set-theory&algebra
normal
partial-order
descriptive
video-solution
0
votes
0
answers
20
views
GATE2015-3-23 Video Solution
Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T$. For any $T, R \in U \text{ let } T \backslash R$ be the set of all elements in ... $X \backslash Y = \phi)$ $\forall X \in U, \forall Y \in U, (X \backslash Y = Y' \backslash X')$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
20
views
gate2015-3
set-theory&algebra
sets
normal
video-solution
0
votes
0
answers
16
views
GATE2017-1-47 Video Solution
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
16
views
gate2017-1
set-theory&algebra
normal
numerical-answers
sets
video-solution
0
votes
0
answers
26
views
GATE2008-IT-28 Video Solution
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
26
views
gate2008-it
set-theory&algebra
lattice
normal
video-solution
0
votes
0
answers
20
views
GATE2014-2-49 Video Solution
The number of distinct positive integral factors of $2014$ is _____________
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
20
views
gate2014-2
set-theory&algebra
easy
numerical-answers
number-theory
video-solution
0
votes
0
answers
29
views
GATE2015-2-9 Video Solution
The number of divisors of $2100$ is ____.
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
29
views
gate2015-2
set-theory&algebra
number-theory
easy
numerical-answers
video-solution
0
votes
0
answers
22
views
GATE2005-IT-33 Video Solution
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $S_2\subset S_1$. What is the maximum cardinality of C? $n$ $n+1$ $2^{n-1} + 1$ $n!$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
22
views
gate2005-it
set-theory&algebra
normal
sets
video-solution
0
votes
0
answers
25
views
GATE2001-2.3 Video Solution
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S1: f(E \cup F) = f(E) \cup f(F)$ $S2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2? Only S1 is correct Only S2 is correct Both S1 and S2 are correct None of S1 and S2 is correct
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
25
views
gate2001
set-theory&algebra
functions
normal
video-solution
0
votes
0
answers
45
views
GATE2003-31 Video Solution
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$, ... for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
45
views
gate2003
set-theory&algebra
partial-order
normal
propositional-logic
video-solution
0
votes
0
answers
19
views
GATE2006-24 Video Solution
Given a set of elements N = {1, 2, ..., n} and two arbitrary subsets A⊆N and B⊆N, how many of the n! permutations $\pi$ from N to N satisfy min($\pi$(A)) = min($\pi$(B)), where min(S) is the smallest integer in the set of integers S, and $\pi$(S) is the set of integers obtained by ... $n! \frac{|A ∩ B|}{|A ∪ B|}$ $\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
19
views
gate2006
set-theory&algebra
normal
sets
video-solution
0
votes
0
answers
24
views
GATE2002-2.17 Video Solution
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
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
24
views
gate2002
set-theory&algebra
normal
relations
video-solution
0
votes
0
answers
19
views
GATE2000-2.5 Video Solution
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having 1 equivalence class $R$ is an equivalence relation having 2 equivalence classes $R$ is an equivalence relation having 3 equivalence classes
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
19
views
gate2000
set-theory&algebra
relations
normal
video-solution
0
votes
0
answers
22
views
GATE1996-2.2 Video Solution
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric
admin
asked
in
Set Theory & Algebra
Apr 18, 2020
by
admin
585
points
22
views
gate1996
set-theory&algebra
relations
normal
video-solution
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