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Most answered questions in Discrete Mathematics
60
votes
6
answers
151
GATE CSE 2014 Set 1 | Question: 50
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 _______.
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
12.4k
views
gatecse-2014-set1
set-theory&algebra
functions
combinatory
numerical-answers
76
votes
6
answers
152
GATE CSE 2008 | Question: 42
$G$ is a graph on $n$ vertices and $2n-2$ edges. The edges of $G$ can be partitioned into two edge-disjoint spanning trees. Which of the following is NOT true for $G$? For every subset of $k$ vertices, the induced subgraph has at ... least $2$ edge-disjoint paths between every pair of vertices. There are at least $2$ vertex-disjoint paths between every pair of vertices.
Akshay Jindal
asked
in
Graph Theory
Sep 27, 2014
by
Akshay Jindal
23.4k
views
gatecse-2008
graph-connectivity
normal
20
votes
6
answers
153
GATE CSE 1998 | Question: 10a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$
Kathleen
asked
in
Set Theory & Algebra
Sep 26, 2014
by
Kathleen
3.7k
views
gate1998
set-theory&algebra
descriptive
relations
36
votes
6
answers
154
GATE CSE 2005 | Question: 7
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
Kathleen
asked
in
Set Theory & Algebra
Sep 22, 2014
by
Kathleen
24.5k
views
gatecse-2005
set-theory&algebra
normal
relations
34
votes
6
answers
155
GATE CSE 2004 | Question: 24
Consider the binary relation: $S= \left\{\left(x, y\right) \mid y=x+1 \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$ The reflexive transitive closure is $S$ ... $\left\{\left(x, y\right) \mid y \leq x \text{ and } x, y \in \left\{0, 1, 2\right\} \right\}$
Kathleen
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Kathleen
9.8k
views
gatecse-2004
set-theory&algebra
easy
relations
54
votes
6
answers
156
GATE CSE 2006 | Question: 26
Which one of the first order predicate calculus statements given below correctly expresses the following English statement? Tigers and lions attack if they are hungry or threatened. ...
Rucha Shelke
asked
in
Mathematical Logic
Sep 18, 2014
by
Rucha Shelke
9.1k
views
gatecse-2006
mathematical-logic
normal
first-order-logic
57
votes
6
answers
157
GATE CSE 2003 | Question: 72
The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE? $((P ∨ R)∧(Q ∨ ¬R))⇒(P ∨ Q)$ ... if $(P ∨ R)∧(Q ∨ ¬R)$ is satisfiable $(P ∨ Q)⇒ \text{FALSE}$ if and only if both $P$ and $Q$ are unsatisfiable
Kathleen
asked
in
Mathematical Logic
Sep 17, 2014
by
Kathleen
14.1k
views
gatecse-2003
mathematical-logic
normal
propositional-logic
44
votes
6
answers
158
GATE CSE 2003 | Question: 39
Let $\Sigma = \left\{a, b, c, d, e\right\}$ be an alphabet. We define an encoding scheme as follows: $g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11$. Let $p_i$ denote the i-th prime number $\left(p_1 = 2\right)$ ... numbers is the encoding, $h$, of a non-empty sequence of strings? $2^73^75^7$ $2^83^85^8$ $2^93^95^9$ $2^{10}3^{10}5^{10}$
Kathleen
asked
in
Set Theory & Algebra
Sep 17, 2014
by
Kathleen
7.5k
views
gatecse-2003
set-theory&algebra
functions
normal
59
votes
6
answers
159
GATE CSE 2003 | Question: 37
Let \(f : A \to B\) be an injective (one-to-one) function. Define \(g : 2^A \to 2^B\) as: \(g(C) = \left \{f(x) \mid x \in C\right\} \), for all subsets $C$ of $A$. Define \(h : 2^B \to 2^A\) as: \(h(D) = \{x \mid x \in A, f(x) \in D\}\), for all ... always true? \(g(h(D)) \subseteq D\) \(g(h(D)) \supseteq D\) \(g(h(D)) \cap D = \phi\) \(g(h(D)) \cap (B - D) \ne \phi\)
Kathleen
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Kathleen
8.1k
views
gatecse-2003
set-theory&algebra
functions
difficult
113
votes
6
answers
160
GATE CSE 2003 | Question: 33
Consider the following formula and its two interpretations \(I_1\) and \(I_2\). \(\alpha: (\forall x)\left[P_x \Leftrightarrow (\forall y)\left[Q_{xy} \Leftrightarrow \neg Q_{yy} \right]\right] \Rightarrow (\forall x)\left[\neg P_x\right]\) \(I_1\) : Domain: ... I_1\) does not Neither \(I_1\) nor \(I_2\) satisfies \(\alpha\) Both \(I_1\) and \(I_2\) satisfies \(\alpha\)
Kathleen
asked
in
Mathematical Logic
Sep 16, 2014
by
Kathleen
15.7k
views
gatecse-2003
mathematical-logic
difficult
first-order-logic
57
votes
6
answers
161
GATE CSE 2003 | Question: 31
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
Kathleen
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Kathleen
11.6k
views
gatecse-2003
set-theory&algebra
partial-order
normal
propositional-logic
29
votes
6
answers
162
GATE CSE 2002 | Question: 2.17
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
Kathleen
asked
in
Set Theory & Algebra
Sep 15, 2014
by
Kathleen
12.8k
views
gatecse-2002
set-theory&algebra
normal
relations
46
votes
6
answers
163
GATE CSE 2002 | Question: 1.4
The minimum number of colours required to colour the vertices of a cycle with $n$ nodes in such a way that no two adjacent nodes have the same colour is $2$ $3$ $4$ $n-2 \left \lfloor \frac{n}{2} \right \rfloor+2$
Kathleen
asked
in
Graph Theory
Sep 15, 2014
by
Kathleen
11.1k
views
gatecse-2002
graph-theory
graph-coloring
normal
37
votes
6
answers
164
GATE CSE 2014 Set 1 | Question: 1
Consider the statement "Not all that glitters is gold Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
6.6k
views
gatecse-2014-set1
mathematical-logic
first-order-logic
52
votes
6
answers
165
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} $
Kathleen
asked
in
Graph Theory
Sep 14, 2014
by
Kathleen
14.0k
views
gatecse-2001
graph-theory
normal
counting
47
votes
6
answers
166
GATE CSE 2000 | Question: 6
Let $S$ be a set of $n$ elements $\left\{1, 2,\ldots, n\right\}$ and $G$ a graph with $2^{n}$ vertices, each vertex corresponding to a distinct subset of $S$. Two vertices are adjacent iff the symmetric difference of the corresponding sets has ... Every vertex in $G$ has the same degree. What is the degree of a vertex in $G$? How many connected components does $G$ have?
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
6.3k
views
gatecse-2000
set-theory&algebra
normal
descriptive
set-theory
33
votes
6
answers
167
GATE CSE 2000 | Question: 5
A multiset is an unordered collection of elements where elements may repeat any number of times. The size of a multiset is the number of elements in it, counting repetitions. What is the number of multisets of size $4$ that can be ... n distinct elements so that at least one element occurs exactly twice? How many multisets can be constructed from n distinct elements?
Kathleen
asked
in
Combinatory
Sep 14, 2014
by
Kathleen
7.8k
views
gatecse-2000
combinatory
normal
descriptive
60
votes
6
answers
168
GATE CSE 2000 | Question: 2.6
Let $P(S)$ denotes the power set of set $S.$ Which of the following is always true? $P(P(S)) = P(S)$ $P(S) ∩ P(P(S)) = \{ Ø \}$ $P(S) ∩ S = P(S)$ $S ∉ P(S)$
Kathleen
asked
in
Set Theory & Algebra
Sep 14, 2014
by
Kathleen
13.4k
views
gatecse-2000
set-theory&algebra
easy
set-theory
39
votes
6
answers
169
GATE CSE 2000 | Question: 1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$
Kathleen
asked
in
Combinatory
Sep 14, 2014
by
Kathleen
9.9k
views
gatecse-2000
easy
pigeonhole-principle
combinatory
78
votes
6
answers
170
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Arjun
asked
in
Mathematical Logic
Sep 2, 2014
by
Arjun
16.4k
views
gate1992
mathematical-logic
normal
first-order-logic
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