Recent questions in Discrete Mathematics / GATE Overflow for GATE CSE

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Function Composition Question Oscar Levin Qn. 20
Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be functions. We can define the composition of $f$ and $g$ to be the function $g \circ f : X \rightarrow Z$ for which the image of each $x \in X$ is $g( f (x))$. That is, plug ... $f$ and $g$? Explain. (d) Suppose $g \circ f$ is surjective. What, if anything, can you say about $f$ and $g$? Explain.

Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be functions. We can define the composition of $f$ and $g$ to be the function $g \circ f : X \rightarrow Z$ for which ...

Deepak Poonia

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Deepak Poonia asked 14 hours ago

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2

ISI PCB 2023 Q3

vbsurya

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vbsurya asked 5 days ago

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3

ISI PCB 2023 Q1
Suppose there are three types of people in the world. A person is honest if the person always speaks the truth. A person is a liar if the person always lies. A person is normal if the person sometimes speaks the truth and sometimes lies. In a city ... . C: B is not normal. Based on the above, deduce with appropriate justifications who among A, B and C has committed the crime.

Suppose there are three types of people in the world.A person is “honest” if the person always speaks the truth. A person is a “liar” if the person always lies. A...

vbsurya

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vbsurya asked 5 days ago

1 votes

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4

ISI PCB 2023 Q2

vbsurya

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vbsurya asked 5 days ago

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5

Kenneth H. Rosen, Chapter 1
When three professors are seated in a restaurant, the hostess asks them: Does everyone want coffee? The first professor says: I do not know. The second professor then says: I do not know. Finally, the third professor says: No, not ... wants coffee. The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee?

When three professors are seated in a restaurant, the hostess asks them: “Does everyone want coffee?” The first professor says: “I do not know.” The second profe...

ENTJ007

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ENTJ007 asked Apr 26

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6

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

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jaydip74 asked Apr 23

1 votes

0 answers

7

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...

yuyutsu

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yuyutsu asked Apr 20

3 votes

2 answers

8

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 ...

akhilroom001

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akhilroom001 asked Apr 20

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1 answer

9

Linear Algebra AX=B
Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly independent columns of B.

Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly in...

Soumya04

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Soumya04 asked Apr 16

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1 answer

10

ISI kolkata MTech CS 2019
Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths from $u$ to $v$ that do not contain the vertex $w$.

Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths fro...

suvasish114

114 views

suvasish114 asked Apr 16

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1 answer

11

self doubt
how to check the validity of an a argument using laws of logics

how to check the validity of an a argument using laws of logics

farhan777

55 views

farhan777 asked Apr 14

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0 answers

12

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...

RahulVerma3

76 views

RahulVerma3 asked Apr 12

2 votes

1 answer

13

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 1
If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then $A=\phi$ $B=\phi$ $A\neq B$ $A=B$

If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then$A=\phi$$B=\phi$$A\neq B$$A=B$

GO Classes

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GO Classes asked Apr 10

1 votes

2 answers

14

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 2
The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?

The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?

GO Classes

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GO Classes asked Apr 10

2 votes

1 answer

15

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 3
What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ? $\{(1, a),(1, b),(2, a),(b, b)\}$ $\{(1,1),(2,2),(a, a),(b, b)\}$ $\{(1, a),(2, a),(1, b),(2, b)\}$ $\{(1,1),(a, a),(2, a),(1, b)\}$

What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ?$\{(1, a),(1, b),(2, a),(b, b)\}$$\{(1,1),(2,2),(a, a),(b, b)\}$$\{(1, a),(2, a),(1, b),(2, b)\}$$\{(1,1),(...

GO Classes

95 views

GO Classes asked Apr 10

3 votes

1 answer

16

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 4
Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then $2^{|A|} \leq|B|$ $2^{|A|} \geq|B|$ $2|A|<|B|$ $2^{|A|} \geq 2^{|B|}$

Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then$2^{|A|} \leq|B|$$2^{|A|} \geq|B|$$2|A|<|B|$$2^{|A|} \geq 2^{|B|}$

GO Classes

89 views

GO Classes asked Apr 10

2 votes

3 answers

17

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 5
Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is: $2^{n^2}$ $\left(2^n\right)^2$ $\left(2^2\right)^n$ None of the above

Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is:$2^{n^2}$$\left(2^n\right)^2$$\left(2^2\right)^n$None of...

GO Classes

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GO Classes asked Apr 10

2 votes

1 answer

18

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 6
Which one of the following is/are true? $R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$ $R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$ $R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$ $R \cap S=(R \cup S) \cup(R-S)$

Which one of the following is/are true?$R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$$R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$$R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$$R \cap S=(R \...

GO Classes

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GO Classes asked Apr 10

3 votes

1 answer

19

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 7
Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasing size ? $|A-B|<|A \oplus B|<|A|+|B|<|A \cup B|$ ... $|A-B|<|A \oplus B|<|A \cup B|<|A|+|B|$

Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasi...

GO Classes

142 views

GO Classes asked Apr 10

7 votes

1 answer

20

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 8
Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is listed in lexicographic order, then the next element after $((1,0), c,(1,1))$ is $((1,0), a,(0,0))$ $((1,1), c,(0,0))$ $((1,1), a,(0,0))$ $((1,1), a,(1,1))$

Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is...

GO Classes

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GO Classes asked Apr 10

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