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Recent questions in Discrete Mathematics
0
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0
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21
#self doubt
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/ Let S={ϕ,{ϕ},{ϕ,{ϕ}}} P(s)= Power Set of set S P(s)={ϕ,{ϕ},{ϕ,{ϕ}},{ϕ,{ϕ,{ϕ}}},{{ϕ},{ϕ,{ϕ}}},{ϕ,{ϕ},{ϕ,{ϕ}}}} n(P(s))=6.
Dknights
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in
Set Theory & Algebra
Feb 6
by
Dknights
112
views
discrete-mathematics
13
votes
1
answer
22
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 15
Let $\mathrm{G}$ be a simple undirected graph on 8 vertices such that there is a vertex of degree 1 , a vertex of degree 2 , a vertex of degree 3 , a vertex of degree 4, a vertex of degree 5 , a vertex of degree 6 and ... of degree 7. Which of the following can be the degree of the last vertex? (Select all that are possible) 0 3 4 8
GO Classes
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in
Graph Theory
Feb 5
by
GO Classes
565
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goclasses2024-mockgate-14
graph-theory
degree-of-graph
multiple-selects
1-mark
3
votes
1
answer
23
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the following statements is/are correct? The function $f$ must be one-to-one. The function $f$ must be onto. The function g must be one-to-one. The function $g$ must be onto.
GO Classes
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in
Set Theory & Algebra
Feb 5
by
GO Classes
464
views
goclasses2024-mockgate-14
set-theory&algebra
functions
multiple-selects
2-marks
6
votes
2
answers
24
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 56
The coefficient of $x^6$ in the expansion of $A(x)$ is, where $ A(x)=\frac{x(1+x)}{(1-x)^3} $
GO Classes
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in
Combinatory
Feb 5
by
GO Classes
501
views
goclasses2024-mockgate-14
numerical-answers
combinatory
recurrence-relation
2-marks
6
votes
1
answer
25
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 57
A strongly connected component $(\mathrm{SCC})$ of a directed graph $\mathrm{G}=(\mathrm{V}, \mathrm{E})$ ... ; edges in its associated directed acyclic graph $G^{\prime}$ be $A, B$ respectively, then what is $A+B?$
GO Classes
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Graph Theory
Feb 5
by
GO Classes
497
views
goclasses2024-mockgate-14
numerical-answers
graph-theory
graph-connectivity
2-marks
11
votes
2
answers
26
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 58
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae. Which of the following is/are True? If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology. If $F \wedge G$ is a contradiction then at ... $G$ is a tautology. If $F \rightarrow G$ is a contradiction then $F$ is a tautology and $G$ is a contradiction.
GO Classes
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Mathematical Logic
Feb 5
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GO Classes
753
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goclasses2024-mockgate-14
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2-marks
1
vote
1
answer
27
Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\) \(\neg x \land y \Rightarrow \neg x \rightarrow y\) \(x \land \neg y \Rightarrow \neg x \rightarrow y\) \(\neg x \land y \Rightarrow y \rightarrow x\)
GO Classes
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in
Mathematical Logic
Feb 4
by
GO Classes
193
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gate2024-da-memory-based
goclasses
mathematical-logic
propositional-logic
0
votes
0
answers
28
Memory Based GATE DA 2024 | Question: 57
First-order logic question: All balls are round except rugby balls.
GO Classes
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Mathematical Logic
Feb 4
by
GO Classes
96
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gate2024-da-memory-based
goclasses
mathematical-logic
first-order-logic
1
vote
0
answers
29
Memory Based GATE DA 2024 | Question: 64
Minimum Number of colors in concentric circles.
GO Classes
asked
in
Graph Theory
Feb 4
by
GO Classes
114
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gate2024-da-memory-based
goclasses
graph-theory
graph-coloring
0
votes
0
answers
30
madeeasy
plz explain option c
nihal_chourasiya
asked
in
Mathematical Logic
Feb 1
by
nihal_chourasiya
94
views
engineering-mathematics
maxima-minima
1
vote
1
answer
31
#self doubt
In the above figure, how many topological sorts are possible, I tried the following method, if we include 5 _ _ _ _ _ for 5 space 5c3 for (2,3,1) then 2 position is 4,0 so a total of 10 if we do like 4 5 _ _ _ _ then only ... GFG the total possible sorts are 13 can someone why this difference is coming ? https://www.geeksforgeeks.org/all-topological-sorts-of-a-directed-acyclic-graph/
Dknights
asked
in
Graph Theory
Jan 31
by
Dknights
130
views
discrete-mathematics
0
votes
1
answer
32
#self doubt
Can someone please explain the following case of combination I means identical D means different DOIB with boxes being empty and non empty As in this question the given value in question itself i am not able to interpret. https://gateoverflow.in/420251/go-classes-test-series-2024-mock-gate-test-12-question-17
Dknights
asked
in
Combinatory
Jan 28
by
Dknights
192
views
discrete-mathematics
3
votes
1
answer
33
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 28
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarily finite cyclic abelian none of the above
GO Classes
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in
Set Theory & Algebra
Jan 28
by
GO Classes
318
views
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
1-mark
4
votes
1
answer
34
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 30
A university's mathematics department has $10$ professors and will offer $20$ different courses next semester. Each professor will be assigned to teach exactly $2$ of the courses, and each course will have exactly one professor assigned to teach it. If any ... $10^{20}-2^{10}$ $\dfrac{20 ! 10 !}{2^{10}}$
GO Classes
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Combinatory
Jan 28
by
GO Classes
512
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goclasses2024-mockgate-13
goclasses
combinatory
counting
1-mark
3
votes
0
answers
35
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 61
Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ ... law $(g+h) \circ f=(g \circ f)+(h \circ f)$. None III only II and III only I, II, and III
GO Classes
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Set Theory & Algebra
Jan 28
by
GO Classes
410
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goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
2-marks
4
votes
1
answer
36
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 62
As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is the set $ [x]_R=\{y \in A \mid x R y\} $ Let's now introduce some ... $\mathrm{I}(\mathrm{R})=n / 2$ and $\mathrm{W}(\mathrm{R})=n / 2$
GO Classes
asked
in
Set Theory & Algebra
Jan 28
by
GO Classes
464
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goclasses2024-mockgate-13
goclasses
set-theory&algebra
set-theory
relations
equivalence-class
2-marks
3
votes
1
answer
37
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 63
For an undirected graph $G$, let $\overline{G}$ refer to the complement (a graph on the same vertex set as $G$, with $(i, j)$ as an edge in $\overline{G}$ if and only if it is not an edge in $G$ ). Consider the following ... is equivalent to (iii) and (v). (i) is equivalent to (ii) and (iv). (i) is equivalent to (ii) and (v)
GO Classes
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in
Graph Theory
Jan 28
by
GO Classes
416
views
goclasses2024-mockgate-13
goclasses
graph-theory
vertex-cover
2-marks
6
votes
2
answers
38
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 17
The number of ways that one can divide $10$ distinguishable objects into $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the piles are also distinguishable?
GO Classes
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Combinatory
Jan 21
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GO Classes
864
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goclasses2024-mockgate-12
goclasses
numerical-answers
combinatory
counting
1-mark
5
votes
2
answers
39
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 18
The number of ways that one can divide $10$ distinguishable objects in $3$ indistinguishable non-empty piles, is: $ \left\{\begin{array}{c} 10 \\ 3 \end{array}\right\}=9330 $ In how many different ways can one do this if the objects are also indistinguishable?
GO Classes
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Combinatory
Jan 21
by
GO Classes
871
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goclasses2024-mockgate-12
goclasses
numerical-answers
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1-mark
2
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1
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40
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 19
Let $\ast $ be the binary operation on the rational numbers given by $a \ast b=a+b+2 a b$. Which of the following are true? $\ast $ is commutative There is a rational number that is a $\ast \;-$ identity. Every rational number has a $\ast \;-$ inverse. I only I and II only I and III only I, II, and III
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Jan 21
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GO Classes
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