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Previous GATE
Featured
Most answered questions in Discrete Mathematics
44
votes
10
answers
21
GATE IT 2005 | Question: 33
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 $C?$ $n$ $n+1$ $2^{n-1} + 1$ $n!$
Ishrat Jahan
asked
in
Set Theory & Algebra
Nov 3, 2014
by
Ishrat Jahan
11.8k
views
gateit-2005
set-theory&algebra
normal
set-theory
29
votes
10
answers
22
GATE CSE 1996 | Question: 2.3
Which of the following is NOT True? (Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication) $((x \rightarrow y) \wedge x) \rightarrow y$ ... $(x \rightarrow (x \vee y))$ $((x \vee y) \leftrightarrow (\neg x \rightarrow \neg y))$
Kathleen
asked
in
Mathematical Logic
Oct 9, 2014
by
Kathleen
8.3k
views
gate1996
mathematical-logic
normal
propositional-logic
100
votes
10
answers
23
GATE CSE 2014 Set 1 | Question: 51
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
26.7k
views
gatecse-2014-set1
graph-theory
numerical-answers
normal
graph-connectivity
40
votes
10
answers
24
GATE CSE 2003 | Question: 38
Consider the set \(\{a, b, c\}\) with binary operators \(+\) and \(*\) defined as follows: ... $(x, y)$ that satisfy the equations) is $0$ $1$ $2$ $3$
Kathleen
asked
in
Set Theory & Algebra
Sep 17, 2014
by
Kathleen
7.0k
views
gatecse-2003
set-theory&algebra
normal
binary-operation
62
votes
10
answers
25
GATE CSE 2002 | Question: 1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
Kathleen
asked
in
Mathematical Logic
Sep 15, 2014
by
Kathleen
14.7k
views
gatecse-2002
mathematical-logic
normal
propositional-logic
27
votes
9
answers
26
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 $S$
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
8.7k
views
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
37
votes
9
answers
27
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 $R_2$
Arjun
asked
in
Set Theory & Algebra
Feb 7, 2019
by
Arjun
17.2k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
12
votes
9
answers
28
ISRO2017-22
Which one of the following Boolean expressions is NOT a tautology? $((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$ $(a \leftrightarrow c) \rightarrow (\sim b\rightarrow (a\wedge c))$ $(a\wedge b \wedge c)\rightarrow (c \vee a)$ $a\rightarrow (b\rightarrow a)$
sh!va
asked
in
Mathematical Logic
May 7, 2017
by
sh!va
7.2k
views
isro2017
mathematical-logic
propositional-logic
44
votes
9
answers
29
GATE CSE 2017 Set 2 | Question: 23
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
Madhav
asked
in
Graph Theory
Feb 14, 2017
by
Madhav
17.3k
views
gatecse-2017-set2
graph-theory
numerical-answers
degree-of-graph
58
votes
9
answers
30
GATE CSE 2017 Set 2 | Question: 47
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
Arjun
asked
in
Combinatory
Feb 14, 2017
by
Arjun
17.6k
views
gatecse-2017-set2
combinatory
generating-functions
numerical-answers
normal
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
11.6k
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
5.1k
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
21.5k
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
8.9k
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
24.5k
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
14.7k
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
11.7k
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
13.1k
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
15.0k
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
9.7k
views
gate1996
set-theory&algebra
functions
normal
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