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Hot questions in Discrete Mathematics
53
votes
8
answers
61
GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
What is the logical translation of the following statement?"None of my friends are perfect."$∃x(F (x)∧ ¬P(x))$$∃ x(¬ F (x)∧ P(x))$$ ∃x(¬F (x)∧¬P(x))$$ ¬�...
Arjun
14.2k
views
Arjun
asked
Sep 24, 2014
Mathematical Logic
gatecse-2013
mathematical-logic
easy
first-order-logic
+
–
50
votes
8
answers
62
GATE CSE 2016 Set 2 | Question: 26
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? ... and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
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:$P:$ $R$ ...
Akash Kanase
14.7k
views
Akash Kanase
asked
Feb 12, 2016
Set Theory & Algebra
gatecse-2016-set2
set-theory&algebra
relations
normal
+
–
65
votes
5
answers
63
GATE CSE 2003 | Question: 8, ISRO2009-53
Let $\text{G}$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $\text{G}$, the number of components in the resultant graph must necessarily lie down between $k$ and $n$ $k-1$ and $k+1$ $k-1$ and $n-1$ $k+1$ and $n-k$
Let $\text{G}$ be an arbitrary graph with $n$ nodes and $k$ components. If a vertex is removed from $\text{G}$, the number of components in the resultant graph must neces...
Kathleen
15.4k
views
Kathleen
asked
Sep 16, 2014
Graph Theory
gatecse-2003
graph-theory
graph-connectivity
normal
isro2009
+
–
33
votes
8
answers
64
GATE IT 2008 | Question: 28
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
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
Ishrat Jahan
15.1k
views
Ishrat Jahan
asked
Oct 28, 2014
Set Theory & Algebra
gateit-2008
set-theory&algebra
lattice
normal
+
–
63
votes
5
answers
65
GATE CSE 2014 Set 3 | Question: 2
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 $X, |f(A \cup B)| = |f(A)| + |f(B)|$ 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 $Y, f^{-1}(S \cap T) = f^{-1}(S) \cap f^{-1}(T)$
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, |f(A \cup B)| = |f(A)| + |f...
go_editor
14.1k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
functions
normal
+
–
14
votes
3
answers
66
GATE CSE 2023 | Question: 39
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as \[ a_{1} \sim a_{2} \text { if } f\left(a_{1}\right)=f\left(a_{2}\right), \] ... is NOT well-defined. $F$ is an onto (or surjective) function. $F$ is a one-to-one (or injective) function. $F$ is a bijective function.
Let $f: A \rightarrow B$ be an onto (or surjective) function, where $A$ and $B$ are nonempty sets. Define an equivalence relation $\sim$ on the set $A$ as\[a_{1} \sim a_{...
admin
5.9k
views
admin
asked
Feb 15, 2023
Set Theory & Algebra
gatecse-2023
set-theory&algebra
equivalence-class
multiple-selects
2-marks
+
–
14
votes
8
answers
67
GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic.$S_1: (\neg p\wedge(p\vee q))\rightarrow q$$S_2: q\rightarrow(\neg p\wedge...
Arjun
8.4k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
+
–
60
votes
6
answers
68
GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true?$P(P(S)) = P(S)$$P(S) ∩ P(P(S)) = \{ Ø \}$$P(S) ∩ S = P(S)$$S ∉ P(S)$
Kathleen
13.6k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2000
set-theory&algebra
easy
set-theory
+
–
56
votes
6
answers
69
GATE CSE 2011 | Question: 30
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$, and a predicate$$P\left(x\right) = \neg \left(x=1\right)\wedge \forall y \left...
go_editor
13.3k
views
go_editor
asked
Sep 29, 2014
Mathematical Logic
gatecse-2011
mathematical-logic
normal
first-order-logic
+
–
27
votes
9
answers
70
GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$
Choose the correct choice(s) regarding the following proportional logic assertion $S$:$$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \righta...
Arjun
8.9k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
+
–
26
votes
6
answers
71
GATE CSE 2022 | Question: 26
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below? $ a_{n} = \left\{\begin{matrix} n + 1, & \text{n is odd} & \\ 1, & \text{otherwise} & \end{matrix}\right.$ ... $\frac{2x}{(1-x^{2})^{2}} + \frac{1}{1-x}$ $\frac{x}{(1-x^{2})^{2}} + \frac{1}{1-x}$
Which one of the following is the closed form for the generating function of the sequence $\{ a_{n} \}_{n \geq 0}$ defined below?$$ a_{n} = \left\{\begin{matrix} n + 1, &...
Arjun
9.5k
views
Arjun
asked
Feb 15, 2022
Combinatory
gatecse-2022
combinatory
generating-functions
2-marks
+
–
57
votes
10
answers
72
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleas...
khushtak
12.2k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set2
mathematical-logic
propositional-logic
+
–
25
votes
9
answers
73
GATE CSE 2017 Set 1 | Question: 47
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
Arjun
11.7k
views
Arjun
asked
Feb 14, 2017
Set Theory & Algebra
gatecse-2017-set1
set-theory&algebra
normal
numerical-answers
set-theory
+
–
29
votes
6
answers
74
GATE CSE 1995 | Question: 1.19
Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above
Let $R$ be a symmetric and transitive relation on a set $A$. Then$R$ is reflexive and hence an equivalence relation$R$ is reflexive and hence a partial order$R$ is reflex...
Kathleen
14.4k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
relations
normal
+
–
51
votes
12
answers
75
GATE CSE 2014 Set 1 | Question: 53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ ... $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE?$(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge...
go_editor
13.7k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
gatecse-2014-set1
mathematical-logic
normal
propositional-logic
+
–
38
votes
9
answers
76
GATE CSE 2019 | Question: 10
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$
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 ...
Arjun
17.4k
views
Arjun
asked
Feb 7, 2019
Set Theory & Algebra
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
+
–
53
votes
6
answers
77
GATE CSE 2001 | Question: 2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices?$\frac{n(n-1)} {2}$$2^n$$n!$$2^\f...
Kathleen
14.2k
views
Kathleen
asked
Sep 14, 2014
Graph Theory
gatecse-2001
graph-theory
normal
counting
+
–
60
votes
9
answers
78
GATE CSE 2005 | Question: 44
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 $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
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 th...
gatecse
13.5k
views
gatecse
asked
Sep 21, 2014
Combinatory
gatecse-2005
set-theory&algebra
normal
pigeonhole-principle
+
–
57
votes
8
answers
79
GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 14
Consider the following popular puzzle. When asked for the ages of her three children, Mrs. Baker says that Alice is her youngest child if Bill is not her youngest child, and that Alice is not her youngest child ... is her youngest child. Carl is her youngest child. Information is not sufficient to find out the youngest child.
Consider the following popular puzzle.When asked for the ages of her three children, Mrs. Baker says that “Alice is her youngest child if Bill is not her youngest child...
GO Classes
3.6k
views
GO Classes
asked
Mar 30, 2022
Mathematical Logic
goclasses2025_cs_wq1
goclasses
mathematical-logic
propositional-logic
2-marks
+
–
39
votes
5
answers
80
GATE CSE 1998 | Question: 1.5
What is the converse of the following assertion? I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go
What is the converse of the following assertion?I stay only if you goI stay if you goIf I stay then you goIf you do not go then I do not stayIf I do not stay then you go
Kathleen
14.0k
views
Kathleen
asked
Sep 25, 2014
Mathematical Logic
gate1998
mathematical-logic
easy
propositional-logic
+
–
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