Recent activity in Engineering Mathematics / GATE Overflow for GATE CSE

3 votes

3 answers

1

UGC NET CSE | December 2013 | Part 2 | Question: 37
Let f and g be the functions from the set of integers defined by $f(x) = 2x+3$ and $g(x) =3x+2$. Then the composition of f and g and g and f is given as 6x+7, 6x+11 6x+11, 6x+7 5x+5, 5x+5 None of the above

Let f and g be the functions from the set of integers defined by $f(x) = 2x+3$ and $g(x) =3x+2$. Then the composition of f and g and g and f is given as6x+7, 6x+116x+11, ...

Deepak Poonia

6.8k views

Deepak Poonia commented 3 hours ago

15 votes

5 answers

2

GATE1991-15,a
Show that the product of the least common multiple and the greatest common divisor of two positive integers $a$ and $b$ is $a\times b$.

Show that the product of the least common multiple and the greatest common divisor of two positive integers $a$ and $b$ is $a\times b$.

Arjun

2.0k views

Arjun edited 4 hours ago

32 votes

2 answers

3

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 7
Let $\mathrm{A}$ be a $3 \times 3$ matrix. Let $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are linearly independent $3$ ... $\mathrm{A}$.

Let $\mathrm{A}$ be a $3 \times 3$ matrix. Let $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are linearly independent $3$-dimensional vectors. Suppose that we have$$A \mathbf{x}=\...

Random_aspirant

1.5k views

Random_aspirant commented 8 hours ago

4 votes

2 answers

4

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 6
The implies connective $\rightarrow$ is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications. Which of the following statements is/are TRUE? For any propositions $P$ ... $R,$ the following statement is always true: $(P \rightarrow Q) \vee (R \rightarrow Q)$.

The “implies” connective “$\rightarrow$” is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications.Which ...

ayushgemini

354 views

ayushgemini answer edited 9 hours ago

1 votes

3 answers

5

GATE CSE 2024 | Set 2 | Question: 50
The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is __________.

Arjun

1.9k views

Arjun edited 12 hours ago

0 votes

1 answer

6

ZEAL test-series : Cardinality of relation!
I know that the number of equivalence relation is bell no. i.e 7th bell no. i.e. 877, but i am not able to find the cardinality of R! Please help!

I know that the number of equivalence relation is bell no. i.e 7th bell no. i.e. 877, but i am not able to find the cardinality of R!Please help!

kingjuno

709 views

kingjuno commented 15 hours ago

0 votes

0 answers

7

Discrete Mathematics | Set Theory | Relation | Equivalance Relation
which if the following statement is True for every set? a. $\exists$ a equivalence class that is also a partition set. b. Every equivalence relation on a set defines a partition of that set. c. $\exists$ a partition of a set that is also equal to equivalence class of the set on some equivalence relation.

which if the following statement is True for every set?a. $\exists$ a equivalence class that is also a partition set.b. Every equivalence relation on a set defines a part...

Shubham Sharma 2

56 views

Shubham Sharma 2 recategorized 19 hours ago

7 votes

4 answers

8

GATE CSE 2024 | Set 2 | Question: 2
Let $p$ and $q$ be the following propositions: $p$ : Fail grade can be given. $q$ : Student scores more than $50 \%$ marks. Consider the statement: "Fail grade cannot be given when student scores more than $50 \%$ marks." ... above statement in propositional logic? $q \rightarrow \neg p$ $q \rightarrow p$ $p \rightarrow q$ $\neg p \rightarrow q$

Let $p$ and $q$ be the following propositions:$p$ : Fail grade can be given.$q$ : Student scores more than $50 \%$ marks.Consider the statement: "Fail grade c...

mo7ammedfarooq

3.4k views

mo7ammedfarooq commented 1 day ago

1 votes

1 answer

9

Why (p ∨ T) is not a tautology?

mo7ammedfarooq

231 views

mo7ammedfarooq commented 1 day ago

10 votes

6 answers

10

GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 3
Consider the following atomic propositions: $\text{R}$: It is Raining $\text{S}$ ... , and vice versa It is raining is equivalent to sonu is sick It is raining or sonu is sick but not both

Consider the following atomic propositions:$\text{R}$: It is Raining$\text{S}$: Sonu is SickWhich of the following is/are correct English Translation of the following log...

Deepak Poonia

683 views

Deepak Poonia commented 1 day ago

12 votes

1 answer

11

GO Classes CS Test Series 2025 | Discrete Mathematics | Topic Wise Test 1| Question: 12
We define a new quantifier, uniqueness quantifier, the symbol of which is $\exists!.$ For any predicate $\text{P}$ and universe $\text{U}, \exists! x \text{P}(x)$ ... I, II, IV I, III II, III, IV IV only

We define a new quantifier, uniqueness quantifier, the symbol of which is $\exists!.$For any predicate $\text{P}$ and universe $\text{U}, \exists! x \text{P}(x)$ means th...

Nalinj

561 views

Nalinj commented 1 day ago

0 votes

0 answers

12

Finite Automata Combined with Relation
Let DFA , M = (Q, ∑, δ, q$_0$, F) and Relation R is defined on Q as R:Q$\rightarrow$Q such that pRq iff $\forall$ w ∈ $\Sigma$* [ δ*(p,w) ∈ F $\leftrightarrow$ δ*(p,w) ∈ F OR δ* (p, w) ∉ F $\leftrightarrow$ δ* (q, w) ∉ F] then ____________ A) R is Reflexive B) R is Symmetric C) R is transitive D) None

Let DFA , M = (Q, ∑, δ, q$_0$, F) and Relation R is defined on Q as R:Q$\rightarrow$Q such that pRq iff $\forall$ w ∈ $\Sigma$* [ δ*(p,w) ∈ F $\leftrightarrow$ δ...

jaydip74

26 views

jaydip74 asked 1 day ago

10 votes

2 answers

13

GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.

Let $X$ be a set and $2^{X}$ denote the powerset of $X$.Define a binary operation $\Delta$ on $2^{X}$ as follows:\[A \Delta B=(A-B) \cup(B-A) \text {. }\]Let $H=\left(2^{...

halfcodeblood

5.7k views

halfcodeblood commented 2 days ago

38 votes

7 answers

14

GATE IT 2008 | Question: 29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the other columns S3 ... solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$

If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of $M$ can be represented as a linear combination of...

Siddhartha_26

9.6k views

Siddhartha_26 commented 2 days ago

13 votes

1 answer

15

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 10
Which of the following statements is /are False? $\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$. $A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3,4\} \subseteq A$ and $\{2,3,4\} \subseteq B$ ... $\{2,3\} \subseteq A \cup B$ implies that if $\{2,3\} \cap A=\emptyset$ then $\{2,3\} \subseteq B$.

Which of the following statements is /are False?$\{2,3,4\} \in A$ and $\{2,3\} \in B$ implies that $\{4\} \subseteq A-B$.$A \cap B \supseteq\{2,3,4\}$ implies that $\{2,3...

Srken

314 views

Srken commented 2 days ago

20 votes

2 answers

16

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 8
Which of the following is/are true? If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$. If $S$ is a set and $|S| = 103$, then $S$ is a power set ... $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.

Which of the following is/are true?If $S$ is a set and $|S| = 103$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.If ...

Srken

306 views

Srken commented 2 days ago

12 votes

3 answers

17

GATE CSE 2024 | Set 1 | Question: 39
Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$? There exist at least $m-n$ linearly independent solutions to this system There exist $m-n$ ... solution in which at least $m-n$ variables are $0$ There exists a solution in which at least $n$ variables are non-zero

Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$?There exist at least $m-n...

Lakshmi Narayana404

3.3k views

Lakshmi Narayana404 commented 2 days ago

1 votes

0 answers

18

Charles C Pinter Abstract Algebra
If G is a group, G=(F(R), +), F(R) set of all real valued functions. H={f€F(R) ; f(-x)=-f(x)} Is H a subgroup of G? My solution.(Click on link..I have not shown th associative prt coz addition is always associative) please let me know if iam correct. https://ibb.co/sPzHg6m https://ibb.co/sPzHg6m

If G is a group, G=(F(R), +), F(R) set of all real valued functions.H={f€F(R) ; f(-x)=-f(x)}Is H a subgroup of G?My solution.(Click on link..I have not shown th associa...

Shubham Sharma 2

43 views

Shubham Sharma 2 retagged 2 days ago

3 votes

2 answers

19

Poset
Consider the poset ({3,5,9,15,24,45},|). Which of the following is correct for the given poset? A. There exists a least element but not a greatest element B. There exists a greatest element but not a least element C. There exists a greatest element and a least element D. There does not exist a greatest element and a least element

Consider the poset ({3,5,9,15,24,45},|). Which of the following is correct for the given poset? A. There exists a least element but not a greatest elementB. There exists ...

Shubham Sharma 2

129 views

Shubham Sharma 2 edited 2 days ago

0 votes

1 answer

20

Question on Quotient set
What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?

What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?

Shubham Sharma 2

91 views

Shubham Sharma 2 retagged 2 days ago

51 votes

12 answers

21

GATE CSE 2014 Set 1 | Question: 53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ ... $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $

Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE?$(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge...

ritiksri8

13.8k views

ritiksri8 commented 3 days ago

33 votes

5 answers

22

GATE CSE 2004 | Question: 70
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above

The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not v...

ritiksri8

7.6k views

ritiksri8 commented 3 days ago

40 votes

9 answers

23

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

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 ...

Deepak Poonia

9.0k views

Deepak Poonia answer edited 3 days ago

6 votes

2 answers

24

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 1
Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”? The columns of $A$ are linearly independent. The rows of $A$ are linearly independent. The only solution of the homogeneous equations $Ax = 0$ is $x = 0$. The rank of $A$ is $n$.

Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”?The columns of $A$ a...

Teet Makor

102 views

Teet Makor answered 3 days ago

4 votes

2 answers

25

GO Classes 2023 | Weekly Quiz 3 | Question: 20
The implies connective $\rightarrow$ is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications. Which of the following statements is/are TRUE? For any propositions $P$ and $Q,$ the following is ... $R,$ the following statement is always true: $(P \rightarrow Q) \vee (R \rightarrow Q)$.

The “implies” connective “$\rightarrow$” is one of the stranger connectives in propositional logic. Below are a series of statements regarding implications. Which...

Dhanush_nindra

548 views

Dhanush_nindra commented 3 days ago

34 votes

4 answers

26

GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 12
Two compound propositions are logically equivalent if they have the same truth table. For example, the following two compound propositions are logically equivalent: $\mathrm{p} \rightarrow \mathrm{q}$ ... propositional variables, how many compound propositions are there that are Not logically equivalent to each other?

Two compound propositions are logically equivalent if they have the same truth table.For example, the following two compound propositions are logically equivalent: $\math...

AjithAddala

1.2k views

AjithAddala answered 3 days ago

4 votes

1 answer

27

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 2
Suppose that $\left\{\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}}, \mathbf{v}_{\mathbf{3}}\right\}$ is a linearly independent set of vectors in $\mathbb{R}^{6}$ ... is linearly independent $\left\{\mathbf{v}_{2}, \mathbf{v}_{3}, \mathbf{w}\right\}$ is linearly independent

Suppose that $\left\{\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}}, \mathbf{v}_{\mathbf{3}}\right\}$ is a linearly independent set of vectors in $\mathbb{R}^{6}$.Furth...

Sachin Mittal 1

68 views

Sachin Mittal 1 answer selected 3 days ago

1 votes

1 answer

28

GO Classes Set Theory And Algebra Practice Set 1 | Question: 7
Define $\mathcal{R}$ the binary relation on $\mathbb{N} \times \mathbb{N}$ to mean $(a, b) \mathcal{R}(c, d)$ iff $b \mid d$ and $a \mid c$

Define $\mathcal{R}$ the binary relation on $\mathbb{N} \times \mathbb{N}$ to mean $(a, b) \mathcal{R}(c, d)$ iff $b \mid d$ and $a \mid c$

yuyutsu

465 views

yuyutsu commented 3 days ago

102 votes

11 answers

29

GATE CSE 2016 Set 2 | Question: 01
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.

Consider the following expressions:$false$$Q$$true$$P\vee Q$$\neg Q\vee P$The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$...

SkillIssue

20.1k views

SkillIssue commented 4 days ago

5 votes

5 answers

30

Kenneth Rosen Edition 6th Exercise 5.5 Question 15 (Page No. 380)
How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 = 21, where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0$\leq$ x1$\leq$10 ?

How many solutions are there to the equationx1 + x2 + x3 + x4 + x5 = 21,where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0$\leq$ x1$\leq$10 ?

Imraan02

10.1k views

Imraan02 commented 4 days ago

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