Most answered questions in Discrete Mathematics / GATE Overflow for GATE CSE

4 votes

1 answer

1801

Discrete Mathematics | Propositional Logic | Test 1 | Question: 3
Statements $P$ and $Q$ are said to be logically equivalent if they have the same truth value in every model. Now, Consider the following statements: i. Sentences $\textit{A provided B}$ and $\textit{(not A) or B}$ ... $(i)$ is correct Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above

Statements $P$ and $Q$ are said to be logically equivalent if they have the same truth value in every model. Now, Consider the following statements: i. Sentences ...

ankitgupta.1729

340 views

ankitgupta.1729 asked Apr 11, 2023

0 votes

1 answer

1802

Discrete Mathematics | Propositional Logic | Test 1 | Question: 4
A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}$. The number of unary Boolean functions is ______

A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}$. The number of unary Boolean functions...

ankitgupta.1729

286 views

ankitgupta.1729 asked Apr 11, 2023

1 votes

1 answer

1803

Discrete Mathematics | Propositional Logic | Test 1 | Question: 5
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it contains no sentential connectives. A sentence $P$ ... ) $\neg P \rightarrow P$ $P \rightarrow \neg P$ $P \vee Q$ $P \vee \neg P$

A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it con...

ankitgupta.1729

251 views

ankitgupta.1729 asked Apr 11, 2023

2 votes

1 answer

1804

Discrete Mathematics | Propositional Logic | Test 1 | Question: 6
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it contains no sentential connectives. Now, consider the following statements: For any ... (iii) are correct (i),(iii) and (iv) are correct (i),(ii) and (iv) are correct

A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it con...

ankitgupta.1729

211 views

ankitgupta.1729 asked Apr 11, 2023

3 votes

1 answer

1805

Discrete Mathematics | Propositional Logic | Test 1 | Question: 8
Consider the following truth table for the connective $\rightarrow:$ ... (i) and (iii) are correct (i) and (ii) are correct (i), (ii) and (iii) are correct

Consider the following truth table for the connective $\rightarrow:$ $$\begin{array}{c|c|c}p & q & p \rightarrow q \\\hlineT & T & T \\T & F & F \\F & T...

ankitgupta.1729

253 views

ankitgupta.1729 asked Apr 11, 2023

3 votes

1 answer

1806

Discrete Mathematics | Propositional Logic | Test 1 | Question: 10
Consider the following two statements: i. Sentence $\textit{Neither A nor B}$ can be represented by $A \downarrow B$ where $\downarrow$ is used in Boolean circuits for $\textit{nor}$ function. ii. Sentence $\textit{not at once A and B}$ ... $(i)$ is correct Only $(ii)$ is correct Both $(i)$ and $(ii)$ are correct None of the above

Consider the following two statements: i. Sentence $\textit{Neither A nor B}$ can be represented by $A \downarrow B$ where $\downarrow$ is used in Boolean circui...

ankitgupta.1729

196 views

ankitgupta.1729 asked Apr 11, 2023

5 votes

1 answer

1807

Discrete Mathematics | Propositional Logic | Test 1 | Question: 11
A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}.$ We denote their totality by the set $\mathbf{B_n}.$ Now, $f \in \mathbf{B_n}$ is called $\textit{linear}$ ... of $\textit{n-ary linear Boolean functions}$ is: $2^{2^n}$ $2^{2^{n+1}}$ $2^n$ $2^{n+1}$

A function $f:\{0,1\}^n \rightarrow \{0,1\}$ is called an $\textit{n-ary Boolean function}$ or $\textit{truth function}.$ We denote their totality by the set $\m...

ankitgupta.1729

459 views

ankitgupta.1729 asked Apr 11, 2023

2 votes

1 answer

1808

Discrete Mathematics | Propositional Logic | Test 1 | Question: 13
The set of logical symbols of a propositional language is called the $\textit{logical signature}.$ A logical signature is called $\textit{functionally complete}$ if every Boolean function is representable by a formula in this ... $\{\rightarrow\}$ is $\textit{not}$ functionally complete.

The set of logical symbols of a propositional language is called the $\textit{logical signature}.$ A logical signature is called $\textit{functionally complete}$ if every...

ankitgupta.1729

292 views

ankitgupta.1729 asked Apr 11, 2023

4 votes

1 answer

1809

Discrete Mathematics | Propositional Logic | Test 1 | Question: 14
A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it contains no sentential connectives. Let $P,Q$ and ... $(P \leftrightarrow P) \leftrightarrow P$ is a tautology Number of correct statements are ______

A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it con...

ankitgupta.1729

316 views

ankitgupta.1729 asked Apr 11, 2023

0 votes

1 answer

1810

Flamingos Fanny and Freddy have three offspring: Happy, Glee, and Joy. These five flamingos are to be distributed to seven different zoos so that no zoo gets both a parent and a child :(. It is not required that every zoo gets a flamingo. In how many different ways can this be done? here if i am using case method on children i am getting a different answer than when i am using case methon on parents, why is that?

Soujit

475 views

Soujit asked Apr 5, 2023

0 votes

1 answer

1811

Discrete-mathematics | Mathematical-logic
Which of the following predicate is/are valid? S1: $\forall x(A(x)\Leftrightarrow B(x))\Rightarrow \exists x(A(x)\Rightarrow B(x))$ S2: $\exists x(A(x)\vee B(x))\Leftrightarrow (\exists xA(x)\vee\exists xB(x))$ A. only S1 B. only S2 C. Both D. None

Which of the following predicate is/are valid? S1: $\forall x(A(x)\Leftrightarrow B(x))\Rightarrow \exists x(A(x)\Rightarrow B(x))$ S2: $\exists x(A(x)\vee B(x))\Le...

Jay Patel 009

371 views

Jay Patel 009 asked Mar 31, 2023

0 votes

1 answer

1812

Dearangements in permutations and combinations
How many derangements of {1, 2, 3, 4, 5, 6, 7} begin with the integers 1, 2, & 3 in some order

How many derangements of {1, 2, 3, 4, 5, 6, 7} begin with the integers 1, 2, & 3 in some order

Aj1202

434 views

Aj1202 asked Mar 30, 2023

6 votes

1 answer

1813

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 4
Select the proposition that is a contradiction. $\neg(p \vee q) \wedge p$ $(p \vee q) \wedge p$ $(\neg p \wedge q) \leftrightarrow p$ $(\neg p \wedge q) \rightarrow p$

Select the proposition that is a contradiction.$\neg(p \vee q) \wedge p$$(p \vee q) \wedge p$$(\neg p \wedge q) \leftrightarrow p$$(\neg p \wedge q) \rightarrow p$

GO Classes

293 views

GO Classes asked Mar 26, 2023

21 votes

1 answer

1814

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 9
Recall the definitions of valid, satisfiable, and unsatisfiable in the propositional logic. What is the relationship between the above concepts? If a formula $\phi$ is valid then $\phi$ is satisfiable; and if $\phi$ is invalid then ... satisfiable, then $\phi$ is invalid; and if $\neg \phi$ is satisfiable then $\phi$ is valid.

Recall the definitions of valid, satisfiable, and unsatisfiable in the propositional logic.What is the relationship between the above concepts?If a formula $\phi$ is vali...

GO Classes

527 views

GO Classes asked Mar 26, 2023

26 votes

1 answer

1815

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 11
A set of propositions is called a system specification. System specification is consistent if they do not contain conflicting requirements that could be used to derive a contradiction. When specifications are not consistent, there ... . Which of the above system specifications are consistent? Only $1$ Only $2$ Both None

A set of propositions is called a system specification.System specification is consistent if they do not contain conflicting requirements that could be used to derive a c...

GO Classes

1.0k views

GO Classes asked Mar 26, 2023

10 votes

1 answer

1816

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 15
If the bank receipt is forged, then Mr. M is liable. If Mr. M is liable, he will go bankrupt. If the bank will loan him money, he will not go bankrupt. The bank will loan him money. Which of the following can ... the above statements? Mr. M is liable The receipt is not forged Mr. M will go bankrupt The bank will go bankrupt

If the bank receipt is forged, then Mr. M is liable.If Mr. M is liable, he will go bankrupt.If the bank will loan him money, he will not go bankrupt.The bank will loan hi...

GO Classes

310 views

GO Classes asked Mar 26, 2023

1 votes

1 answer

1817

GO Classes 2023 | IIITH Mock Test 1 | Question: 1
Let $\text{R}$ be a relation from a set $\text{A}$ to a set $\text{B}.$ The inverse relation from $\text{B}$ to $\text{A},$ denoted by $\text{R}^{-1},$ is the set of ordered pairs $\{(b,a) \mid (a,b) \in R\}$ ... $\text{S1}$ Only $\text{S2}$ Both $\text{S1}$ and $\text{S2}$ None of the above

Let $\text{R}$ be a relation from a set $\text{A}$ to a set $\text{B}.$ The inverse relation from $\text{B}$ to $\text{A},$ denoted by $\text{R}^{-1},$ is the set of orde...

GO Classes

765 views

GO Classes asked Mar 26, 2023

1 votes

1 answer

1818

GO Classes 2023 | IIITH Mock Test 1 | Question: 5
$(\text{Q}, \ast)$ is an algebraic structure where $\text{Q}$ represents rational numbers and $\ast$ denotes multiplication. Which one of the following statements is true? $\text{Q}$ is an abelian group. $\text{Q}$ is a group but not abelian. $\text{Q}$ is a semigroup but not a monoid. $\text{Q}$ is monoid but not group.

$(\text{Q}, \ast)$ is an algebraic structure where $\text{Q}$ represents rational numbers and $\ast$ denotes multiplication. Which one of the following statements is true...

GO Classes

660 views

GO Classes asked Mar 26, 2023

2 votes

1 answer

1819

GO Classes 2023 | IIITH Mock Test 1 | Question: 33
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ where $a_n = \binom {n+4}{n}$ for $n= 0,1,2,\ldots ?$ $\frac{1}{(1-x)^5}$ $\frac{5}{(1-x)}$ $\frac{1}{(1-x)^4}$ $\frac{x}{(1-x)^5}$

Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ where $a_n = \binom {n+4}{n}$ for $n= 0,1,2,\ldots ?$$\frac{1...

GO Classes

656 views

GO Classes asked Mar 26, 2023

3 votes

1 answer

1820

GO Classes 2023 | IIITH Mock Test 1 | Question: 42
Which of the following statements are correct? The complement of a simple disconnected graph must be connected. The complement of a simple connected graph must be disconnected. The complement of complete bipartite graph $\text{K}(4,6)$ has $10$ components. ... its complement. Then $\text{G}$ must have $4k$ or $4k + 1$ vertices for some integer $k.$

Which of the following statements are correct?The complement of a simple disconnected graph must be connected.The complement of a simple connected graph must be disconnec...

GO Classes

560 views

GO Classes asked Mar 26, 2023

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