search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

Recent questions in Discrete Mathematics

5 votes
2 answers
1
Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ to the set $\{0, 1, 2\}$ Which of the following ... to $S_2$ There exists a surjection from $S_1$ to $S_2$ There exists a bijection from $S_1$ to $S_2$ There does not exist an injection from $S_1$ to $S_2$
asked Feb 18 in Set Theory & Algebra Arjun 1.1k views
4 votes
3 answers
2
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 $S$
asked Feb 18 in Mathematical Logic Arjun 954 views
2 votes
1 answer
3
For two $n$-dimensional real vectors $P$ and $Q$, the operation $s(P,Q)$ is defined as follows: $s(P,Q) = \displaystyle \sum_{i=1}^n (P[i] \cdot Q[i])$ Let $\mathcal{L}$ be a set of $10$-dimensional non-zero real vectors such that for every pair of distinct vectors $P,Q \in \mathcal{L}$, $s(P,Q)=0$. What is the maximum cardinality possible for the set $\mathcal{L}$? $9$ $10$ $11$ $100$
asked Feb 18 in Set Theory & Algebra Arjun 767 views
5 votes
5 answers
4
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
asked Feb 18 in Combinatory Arjun 1.7k views
2 votes
4 answers
5
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 $S_2$ are tautologies ... tautology 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
asked Feb 18 in Mathematical Logic Arjun 879 views
2 votes
3 answers
6
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.
asked Feb 18 in Graph Theory Arjun 1.2k views
6 votes
2 answers
7
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
asked Feb 18 in Combinatory Arjun 1.5k views
5 votes
4 answers
8
Let $G$ be a group of order $6$, and $H$ be a subgroup of $G$ such that $1<|H|<6$. Which one of the following options is correct? Both $G$ and $H$ are always cyclic $G$ may not be cyclic, but $H$ is always cyclic $G$ is always cyclic, but $H$ may not be cyclic Both $G$ and $H$ may not be cyclic
asked Feb 18 in Set Theory & Algebra Arjun 1.2k views
9 votes
5 answers
9
Let $G=(V, E)$ be an undirected unweighted connected graph. The diameter of $G$ is defined as: $\text{diam}(G)=\displaystyle \max_{u,v\in V} \{\text{the length of shortest path between $u$ and $v$}\}$ Let $M$ be the adjacency matrix of $G$. Define graph $G_2$ on the same set of ... $\text{diam}(G_2) = \text{diam}(G)$ $\text{diam}(G)< \text{diam}(G_2)\leq 2\; \text{diam}(G)$
asked Feb 18 in Graph Theory Arjun 1.1k views
3 votes
5 answers
10
A relation $R$ is said to be circular if $a\text{R}b$ and $b\text{R}c$ together imply $c\text{R}a$. Which of the following options is/are correct? If a relation $S$ is reflexive and symmetric, then $S$ is an equivalence relation. If a relation $S$ ... $S$ is an equivalence relation. If a relation $S$ is transitive and circular, then $S$ is an equivalence relation.
asked Feb 18 in Set Theory & Algebra Arjun 1k views
3 votes
3 answers
11
Let G(V,E) be a simple graph. Let G’(V,E’) be a graph obtained from G such that (u,v) is an edge in G’ if (u,v) is not an edge in G. Which of the following is true? At least one of G or G’ are connected. G is necessarily disconnected. Both G and G’ are disconnected. None of the above.
asked Feb 15 in Graph Theory vivek_mishra 228 views
1 vote
0 answers
12
For two n-bit strings x, y ∈ {0, 1}n, define z := x ⊕ y to be the bitwise XOR of the two strings (that is, if xi, yi, zi denote the i-th bits of x, y, z respectively, then zi = xi + yi mod 2). A function h : {0, 1}n → {0, 1}n is called linear if h(x ⊕ y) = h(x) ⊕ h(y), for every x, y ∈ {0, 1}n. The number of such linear functions for n ≥ 2: 2^n 2^2n 2^(n+1) n
asked Feb 15 in Combinatory vivek_mishra 200 views
1 vote
3 answers
13
The number of positive integers not exceeding $100$ that are either odd or the square of an integer is _______ $63$ $59$ $55$ $50$
asked Nov 20, 2020 in Set Theory & Algebra jothee 954 views
2 votes
2 answers
14
How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books? $4$ $6$ $7$ $9$
asked Nov 20, 2020 in Combinatory jothee 834 views
1 vote
2 answers
15
Which of the following pairs of propositions are not logically equivalent? $((p \rightarrow r) \wedge (q \rightarrow r))$ and $((p \vee q) \rightarrow r)$ $p \leftrightarrow q$ and $(\neg p \leftrightarrow \neg q)$ $((p \wedge q) \vee (\neg p \wedge \neg q))$ and $p \leftrightarrow q$ $((p \wedge q) \rightarrow r)$ and $((p \rightarrow r) \wedge (q \rightarrow r))$
asked Nov 20, 2020 in Discrete Mathematics jothee 744 views
0 votes
1 answer
16
Let $G$ be a directed graph whose vertex set is the set of numbers from $1$ to $100$. There is an edge from a vertex $i$ to a vertex $j$ if and only if either $j=i+1$ or $j=3i$. The minimum number of edges in a path in $G$ from vertex $1$ to vertex $100$ is ______ $23$ $99$ $4$ $7$
asked Nov 20, 2020 in Discrete Mathematics jothee 236 views
0 votes
1 answer
17
If $f(x)=x$ is my friend, and $p(x) =x$ is perfect, then correct logical translation of the statement “some of my friends are not perfect” is ______ $\forall _x (f(x) \wedge \neg p(x))$ $\exists _x (f(x) \wedge \neg p(x))$ $\neg (f(x) \wedge \neg p(x))$ $\exists _x (\neg f(x) \wedge \neg p(x))$
asked Nov 20, 2020 in Discrete Mathematics jothee 245 views
0 votes
1 answer
18
What kind of clauses are available in conjunctive normal form? Disjunction of literals Disjunction of variables Conjunction of literals Conjunction of variables
asked Nov 20, 2020 in Discrete Mathematics jothee 282 views
0 votes
2 answers
19
Consider the following properties: Reflexive Antisymmetric Symmetric Let $A=\{a,b,c,d,e,f,g\}$ and $R=\{(a,a), (b,b), (c,d), (c,g), (d,g), (e,e), (f,f), (g,g)\}$ be a relation on $A$. Which of the following property (properties) is (are) satisfied by the relation $R$? Only $a$ Only $c$ Both $a$ and $b$ $b$ and not $a$
asked Nov 20, 2020 in Discrete Mathematics jothee 268 views
0 votes
1 answer
20
Consider the following argument with premise $\forall _x (P(x) \vee Q(x))$ and conclusion $(\forall _x P(x)) \wedge (\forall _x Q(x))$ ... valid argument Steps $(C)$ and $(E)$ are not correct inferences Steps $(D)$ and $(F)$ are not correct inferences Step $(G)$ is not a correct inference
asked Nov 20, 2020 in Discrete Mathematics jothee 171 views
...