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Previous GATE
Featured
Highest voted questions in Discrete Mathematics
41
votes
9
answers
121
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
41
votes
5
answers
122
GATE CSE 1996 | Question: 8
Let $F$ be the collection of all functions $f: \{1, 2, 3\} \to \{1, 2, 3\}$. If $f$ and $g \in F$, define an equivalence relation $\sim$ by $f\sim g$ if and only if $f(3) = g(3)$. Find the number of equivalence classes defined by $\sim$. Find the number of elements in each equivalence class.
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
6.0k
views
gate1996
set-theory&algebra
relations
functions
normal
descriptive
41
votes
9
answers
123
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
9.6k
views
gate1996
set-theory&algebra
functions
normal
41
votes
4
answers
124
GATE CSE 1995 | Question: 2.19
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is True Multiple Values False Cannot be determined
Kathleen
asked
in
Mathematical Logic
Oct 8, 2014
by
Kathleen
8.5k
views
gate1995
mathematical-logic
normal
propositional-logic
41
votes
3
answers
125
GATE CSE 1994 | Question: 1.10
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$? $g=g^{-1} \text{ for every } g \in G$ $g=g^2 \text{ for every }g \in G$ $(goh)^2 = g^2oh^2 \text{ for every } g, h \in G$ $G$ is of finite order
Kathleen
asked
in
Set Theory & Algebra
Oct 4, 2014
by
Kathleen
10.6k
views
gate1994
set-theory&algebra
group-theory
normal
41
votes
2
answers
126
GATE CSE 2014 Set 3 | Question: 3
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________.
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
8.4k
views
gatecse-2014-set3
set-theory&algebra
group-theory
numerical-answers
normal
41
votes
5
answers
127
GATE CSE 2012 | Question: 37
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set? $ 2^{n}$ $2^{n} – 1$ $2^{n} – 2$ $2(2^{n} – 2)$
gatecse
asked
in
Set Theory & Algebra
Sep 26, 2014
by
gatecse
9.3k
views
gatecse-2012
set-theory&algebra
functions
normal
41
votes
3
answers
128
GATE CSE 2007 | Question: 26
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:
Kathleen
asked
in
Set Theory & Algebra
Sep 21, 2014
by
Kathleen
13.3k
views
gatecse-2007
set-theory&algebra
normal
partial-order
descriptive
40
votes
6
answers
129
GATE CSE 2019 | Question: 38
Let $G$ be any connected, weighted, undirected graph. $G$ has a unique minimum spanning tree, if no two edges of $G$ have the same weight. $G$ has a unique minimum spanning tree, if, for every cut of $G$, there is a unique minimum-weight edge crossing the cut. Which of the following statements is/are TRUE? I only II only Both I and II Neither I nor II
Arjun
asked
in
Graph Theory
Feb 7, 2019
by
Arjun
20.4k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
2-marks
40
votes
2
answers
130
TIFR CSE 2012 | Part A | Question: 8
How many pairs of sets $(A, B)$ are there that satisfy the condition $A, B \subseteq \left\{1, 2,...,5\right\}, A \cap B = \{\}?$ $125$ $127$ $130$ $243$ $257$
makhdoom ghaya
asked
in
Set Theory & Algebra
Oct 26, 2015
by
makhdoom ghaya
3.1k
views
tifr2012
set-theory&algebra
set-theory
40
votes
5
answers
131
TIFR CSE 2010 | Part A | Question: 18
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ? $2^{n+1}$ $2^{2n}$ $3^{n}$ $2^{n} + 1$ $3^{n + 1}$
makhdoom ghaya
asked
in
Set Theory & Algebra
Oct 4, 2015
by
makhdoom ghaya
4.6k
views
tifr2010
set-theory
40
votes
5
answers
132
GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
13.9k
views
gate1996
set-theory&algebra
relations
normal
40
votes
7
answers
133
GATE CSE 2005 | Question: 43
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto
gatecse
asked
in
Set Theory & Algebra
Sep 21, 2014
by
gatecse
9.9k
views
gatecse-2005
set-theory&algebra
functions
normal
40
votes
7
answers
134
GATE CSE 2010 | Question: 28
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? $7, 6, 5, 4, 4, 3, 2, 1$ $6, 6, 6, 6, 3, 3, 2, 2$ $7, 6, 6, 4, 4, 3, 2, 2$ $8, 7, 7, 6, 4, 2, 1, 1$ I and II III and IV IV only II and IV
gatecse
asked
in
Graph Theory
Sep 21, 2014
by
gatecse
18.4k
views
gatecse-2010
graph-theory
degree-of-graph
40
votes
10
answers
135
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
40
votes
8
answers
136
GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
8.4k
views
gatecse-2009
mathematical-logic
easy
first-order-logic
40
votes
9
answers
137
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
8.8k
views
gatecse-2009
set-theory&algebra
normal
group-theory
40
votes
4
answers
138
GATE CSE 1992 | Question: 14a
If $G$ is a group of even order, then show that there exists an element $a≠e$, the identity in $G$, such that $a^2 = e$.
Kathleen
asked
in
Set Theory & Algebra
Sep 13, 2014
by
Kathleen
7.1k
views
gate1992
set-theory&algebra
group-theory
normal
descriptive
proof
39
votes
5
answers
139
GATE CSE 2017 Set 2 | Question: 24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
14.3k
views
gatecse-2017-set2
polynomials
numerical-answers
set-theory&algebra
39
votes
4
answers
140
GATE CSE 1994 | Question: 2.2
On the set $N$ of non-negative integers, the binary operation ______ is associative and non-commutative.
Kathleen
asked
in
Set Theory & Algebra
Oct 4, 2014
by
Kathleen
5.8k
views
gate1994
set-theory&algebra
normal
group-theory
binary-operation
fill-in-the-blanks
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