Recent questions tagged set-theory / GATE Overflow for GATE CSE

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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

41 views

RahulVerma3 asked Apr 12

1 votes

1 answer

2

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

32 views

GO Classes asked Apr 10

1 votes

2 answers

3

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

32 views

GO Classes asked Apr 10

2 votes

1 answer

4

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

30 views

GO Classes asked Apr 10

3 votes

1 answer

5

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

33 views

GO Classes asked Apr 10

2 votes

3 answers

6

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

36 views

GO Classes asked Apr 10

1 votes

1 answer

7

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

18 views

GO Classes asked Apr 10

3 votes

1 answer

8

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

48 views

GO Classes asked Apr 10

5 votes

1 answer

9

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

55 views

GO Classes asked Apr 10

3 votes

0 answers

10

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 9
Which of the following statements is $\textbf{TRUE}$? For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=A-(B \cup C)$. For all sets $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.

Which of the following statements is $\textbf{TRUE}$?For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$.For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$.For all sets ...

GO Classes

46 views

GO Classes asked Apr 10

1 votes

0 answers

11

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 10
Which of the following statements is $\textbf{FALSE}$? $C-(B \cup A)=(C-B)-A$ $A-(C \cup B)=(A-B)-C$ $B-(A \cup C)=(B-C)-A$ $A-(B \cup C)=(B-C)-A$

Which of the following statements is $\textbf{FALSE}$?$C-(B \cup A)=(C-B)-A$$A-(C \cup B)=(A-B)-C$$B-(A \cup C)=(B-C)-A$$A-(B \cup C)=(B-C)-A$

GO Classes

33 views

GO Classes asked Apr 10

3 votes

1 answer

12

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 1
What is the Cardinality of the Power set of the set $\{0,1,2\}$? $8$ $6$ $7$ $9$

What is the Cardinality of the Power set of the set $\{0,1,2\}$?$8$$6$$7$$9$

GO Classes

53 views

GO Classes asked Apr 3

3 votes

1 answer

13

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 2
The symmetric difference of sets $\text{A}=\{1,2, 3,4, 5, 6, 7, 8\}$ and $\text{B}= \{1, 3, 5, 6, 7,8,9\}$ is: $\{1, 3, 5, 6, 7,8\}$ $\{2, 4, 9\}$ $\{2, 4\}$ $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$

The symmetric difference of sets $\text{A}=\{1,2, 3,4, 5, 6, 7, 8\}$ and $\text{B}= \{1, 3, 5, 6, 7,8,9\}$ is:$\{1, 3, 5, 6, 7,8\}$$\{2, 4, 9\}$$\{2, 4\}$$\{1, 2, 3, 4, 5...

GO Classes

45 views

GO Classes asked Apr 3

3 votes

1 answer

14

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 3
If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to $\{u,v,w,x\}$ $\{ x \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$

If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to$\{u,v,w,x\}$$\{ x \}$$\{u,v,w,x...

GO Classes

79 views

GO Classes asked Apr 3

5 votes

1 answer

15

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 4
The power set of the set $\{ \Phi \}$ is $\{ \Phi \}$ $\{ \Phi, \{ \Phi \} \}$ $\{ 0 \}$ $\{ 0, \Phi , \{ \Phi \} \}$

The power set of the set $\{ \Phi \}$ is$\{ \Phi \}$$\{ \Phi, \{ \Phi \} \}$$\{ 0 \}$$\{ 0, \Phi , \{ \Phi \} \}$

GO Classes

51 views

GO Classes asked Apr 3

5 votes

1 answer

16

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 5
Let $A, B$ be two sets. Let $\bar{A}$ denote the complement of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are not in $B$. Set $(A - (A - B))$ is equal to: $B$ $A\cap \bar{B}$ $A - B$ $A\cap B$

Let $A, B$ be two sets. Let $\bar{A}$ denote the complement of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are n...

GO Classes

66 views

GO Classes asked Apr 3

5 votes

2 answers

17

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 6
Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Then at least one of the sets $S_i$ is a finite set not more than one of the sets $S_i$ can be finite at least one of the sets $S_i$ is an infinite None of the above

Let $S$ be an infinite set and $S_1 \dots , S_n$ be sets such that $S_1 \cup S_2 \cup \dots \cup S_n = S$. Thenat least one of the sets $S_i$ is a finite setnot more than...

GO Classes

70 views

GO Classes asked Apr 3

11 votes

1 answer

18

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 7
Power set of empty set has exactly _______ subsets. One Two Zero Three

Power set of empty set has exactly _______ subsets.OneTwoZeroThree

GO Classes

174 views

GO Classes asked Apr 3

20 votes

2 answers

19

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 ...

GO Classes

225 views

GO Classes asked Apr 3

6 votes

1 answer

20

GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 9
Which of the following statements is /are TRUE? $2 \in A \cup B$ implies that if $2 \notin A$ then $2 \in B$. $\{2,3\} \subseteq A$ implies that $2 \in A$ and $3 \in A$. $A \cap B \supseteq\{2,3\}$ ... $A-B \supseteq\{3\}$ and $\{2\} \subseteq B$ implies that $\{2,3\} \subseteq A \cup B$.

Which of the following statements is /are TRUE?$2 \in A \cup B$ implies that if $2 \notin A$ then $2 \in B$.$\{2,3\} \subseteq A$ implies that $2 \in A$ and $3 \in A$.$A ...

GO Classes

63 views

GO Classes asked Apr 3

12 votes

1 answer

21

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...

GO Classes

230 views

GO Classes asked Apr 3

4 votes

1 answer

22

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 62
As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is the set $ [x]_R=\{y \in A \mid x R y\} $ Let's now introduce some ... $\mathrm{I}(\mathrm{R})=n / 2$ and $\mathrm{W}(\mathrm{R})=n / 2$

As a refresher, if $R$ is an equivalence relation over a set $A$ and $x \in A$, then the equivalence class of $\boldsymbol{x}$ in $\boldsymbol{R}$, denoted $[x]_R,$ is th...

GO Classes

493 views

GO Classes asked Jan 28

8 votes

1 answer

23

GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 12
Let $A-B$ denote $\{x \in A: x \notin B\}$. If $(A-B) \cup B=A$, which of the following must be true? $B$ is empty $A \subseteq B$ $B \subseteq A$ $(B-A) \cup A=B$

Let $A-B$ denote $\{x \in A: x \notin B\}$. If $(A-B) \cup B=A$, which of the following must be true?$B$ is empty$A \subseteq B$$B \subseteq A$$(B-A) \cup A=B$

GO Classes

627 views

GO Classes asked Jan 13

0 votes

1 answer

24

GATE 2018 | MATHS | Q-40
Which one of the following statements is true? (A) Every group of order 12 has a non-trivial proper normal subgroup (B) Some group of order 12 does not have a non-trivial proper normal subgroup (C) Every group of order 12 has a subgroup of order 6 (D) Every group of order 12 has an element of order 12

Which one of the following statements is true?(A) Every group of order 12 has a non-trivial proper normal subgroup(B) Some group of order 12 does not have a non-trivial p...

rajveer43

122 views

rajveer43 asked Jan 11

1 votes

0 answers

25

GATE 2019 | maths | set theory
Consider the following statements: I.The set $ \mathbb{R} $ is uncountable. II.The set $ \{ f : f \text{ is a function from } \mathbb{N} \text{ to } \{0, 1\} \} $ is uncountable. III.The set $ \{ p : p \text{ is a prime number} \} $ is uncountable. ... of the above statements are TRUE? (A)] I and IV only (B) II and IV only (C) II and III only (D) I, II, and IV only

Consider the following statements: I.The set $ \mathbb{R} $ is uncountable.II.The set $ \{ f : f \text{ is a function from } \mathbb{N} \text{ to } \{0, 1\} \} $ is uncou...

rajveer43

73 views

rajveer43 asked Jan 10

0 votes

0 answers

26

GATE 2021 | MATHS | Q-20
Let $ f: \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \to \mathbb{R} $ be given by $ f(x) = \frac{\pi}{2} + x - \tan^{-1}(x) $. Consider the following statements: $P:$ $ |f(x) - f(y)| < |x - y| $ ... Then the correct option is: (A) both P and Q are TRUE (B) P is TRUE and Q is FALSE (C) P is FALSE and Q is TRUE (D) both P and Q are FALSE

Let $ f: \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \to \mathbb{R} $ be given by $ f(x) = \frac{\pi}{2} + x - \tan^{-1}(x) $. Consider the following statements: $P:$...

rajveer43

66 views

rajveer43 asked Jan 10

0 votes

1 answer

27

GATE 2023 | Maths | Sample Ques for CS-IT
Let $G$ be an abelian group and $\Phi: G \rightarrow (\mathbb{Z}, +)$ be a surjective group homomorphism. Let $1 = \Phi(a)$ for some $a \in G$. Consider the following statements: $P$: For every $g \in G$, there exists an $n \in \ ... following statements is/are correct? (A) \(P$ is TRUE (B) $P$ is FALSE (C) $Q$ is TRUE (D) $Q$ is FALSE

Let $G$ be an abelian group and $\Phi: G \rightarrow (\mathbb{Z}, +)$ be a surjective group homomorphism. Let $1 = \Phi(a)$ for some $a \in G$.Consider the follow...

rajveer43

75 views

rajveer43 asked Jan 10

1 votes

1 answer

28

Made Easy
What is meant by refinement that has been asked in this following question?

What is meant by refinement that has been asked in this following question?

Rohit Chakraborty

417 views

Rohit Chakraborty asked Oct 6, 2023

0 votes

1 answer

29

Discrete Mathematics | Set Theory | Equivalent Relation

Debargha Mitra Roy

202 views

Debargha Mitra Roy asked Sep 23, 2023

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