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Featured
Most answered questions in Discrete Mathematics
25
votes
9
answers
31
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 ____________ .
Arjun
asked
in
Set Theory & Algebra
Feb 14, 2017
by
Arjun
11.5k
views
gatecse-2017-set1
set-theory&algebra
normal
numerical-answers
set-theory
23
votes
9
answers
32
GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
makhdoom ghaya
asked
in
Mathematical Logic
Nov 14, 2016
by
makhdoom ghaya
5.0k
views
gate1987
mathematical-logic
propositional-logic
proof
descriptive
91
votes
9
answers
33
GATE CSE 2016 Set 1 | Question: 28
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 ___________.
Sandeep Singh
asked
in
Set Theory & Algebra
Feb 12, 2016
by
Sandeep Singh
21.3k
views
gatecse-2016-set1
set-theory&algebra
functions
normal
numerical-answers
9
votes
9
answers
34
Kenneth Rosen Edition 6 Question 45 (Page No. 346)
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?
Anu
asked
in
Combinatory
Jul 13, 2015
by
Anu
8.8k
views
combinatory
counting
32
votes
9
answers
35
GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
makhdoom ghaya
asked
in
Graph Theory
Feb 13, 2015
by
makhdoom ghaya
24.3k
views
gatecse-2015-set1
graph-theory
graph-connectivity
normal
graph-planarity
numerical-answers
50
votes
9
answers
36
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Ishrat Jahan
asked
in
Mathematical Logic
Nov 3, 2014
by
Ishrat Jahan
14.5k
views
gateit-2005
mathematical-logic
first-order-logic
normal
41
votes
9
answers
37
GATE IT 2004 | Question: 31
Let $p, q, r$ and $s$ be four primitive statements. Consider the following arguments: $P: [(¬p\vee q) ∧ (r → s) ∧ (p \vee r)] → (¬s → q)$ $Q: [(¬p ∧q) ∧ [q → (p → r)]] → ¬r$ $R: [[(q ∧ r) → p] ∧ (¬q \vee p)] → r$ $S: [p ∧ (p → r) ∧ (q \vee ¬ r)] → q$ Which of the above arguments are valid? $P$ and $Q$ only $P$ and $R$ only $P$ and $S$ only $P, Q, R$ and $S$
Ishrat Jahan
asked
in
Mathematical Logic
Nov 2, 2014
by
Ishrat Jahan
11.6k
views
gateit-2004
mathematical-logic
normal
propositional-logic
64
votes
9
answers
38
GATE IT 2006 | Question: 25
Consider the undirected graph $G$ defined as follows. The vertices of $G$ are bit strings of length $n$. We have an edge between vertex $u$ and vertex $v$ if and only if $u$ and $v$ differ in exactly one bit position (in other words, $v$ can be obtained from $u$ by ... $\left(\frac{1}{n}\right)$ $\left(\frac{2}{n}\right)$ $\left(\frac{3}{n}\right)$
Ishrat Jahan
asked
in
Graph Theory
Oct 31, 2014
by
Ishrat Jahan
13.0k
views
gateit-2006
graph-theory
graph-coloring
normal
68
votes
9
answers
39
GATE IT 2008 | Question: 21
Which of the following first order formulae is logically valid? Here $\alpha(x)$ is a first order formula with $x$ as a free variable, and $\beta$ ... $[(\forall x, \alpha(x)) \rightarrow \beta] \rightarrow [\forall x, \alpha(x) \rightarrow \beta]$
Ishrat Jahan
asked
in
Mathematical Logic
Oct 27, 2014
by
Ishrat Jahan
14.8k
views
gateit-2008
first-order-logic
normal
41
votes
9
answers
40
GATE CSE 1996 | Question: 2.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
9.5k
views
gate1996
set-theory&algebra
functions
normal
38
votes
9
answers
41
GATE CSE 2014 Set 2 | Question: 3
The maximum number of edges in a bipartite graph on $12$ vertices is____
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
26.9k
views
gatecse-2014-set2
graph-theory
graph-connectivity
numerical-answers
normal
60
votes
9
answers
42
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 $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
gatecse
asked
in
Combinatory
Sep 21, 2014
by
gatecse
13.2k
views
gatecse-2005
set-theory&algebra
normal
pigeonhole-principle
65
votes
9
answers
43
GATE CSE 2004 | Question: 75
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$
Kathleen
asked
in
Combinatory
Sep 18, 2014
by
Kathleen
16.4k
views
gatecse-2004
combinatory
76
votes
9
answers
44
GATE CSE 2006 | Question: 25
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left | \left\{j \mid i\in X_j \right\} \right|$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Rucha Shelke
10.9k
views
gatecse-2006
set-theory&algebra
normal
functions
65
votes
9
answers
45
GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$
Kathleen
asked
in
Graph Theory
Sep 17, 2014
by
Kathleen
15.5k
views
gatecse-2003
graph-theory
normal
degree-of-graph
60
votes
9
answers
46
GATE CSE 2003 | Question: 36
How many perfect matching are there in a complete graph of $6$ vertices? $15$ $24$ $30$ $60$
Kathleen
asked
in
Graph Theory
Sep 16, 2014
by
Kathleen
43.7k
views
gatecse-2003
graph-theory
graph-matching
normal
23
votes
9
answers
47
GATE CSE 2003 | Question: 34
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$
Kathleen
asked
in
Combinatory
Sep 16, 2014
by
Kathleen
11.1k
views
gatecse-2003
combinatory
balls-in-bins
normal
40
votes
9
answers
48
GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
gatecse
asked
in
Set Theory & Algebra
Sep 15, 2014
by
gatecse
8.7k
views
gatecse-2009
set-theory&algebra
normal
group-theory
38
votes
9
answers
49
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
Kathleen
asked
in
Combinatory
Sep 14, 2014
by
Kathleen
12.4k
views
gatecse-2001
combinatory
normal
39
votes
9
answers
50
GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above
Kathleen
asked
in
Mathematical Logic
Sep 12, 2014
by
Kathleen
8.6k
views
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
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