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Recent questions tagged set-theory

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1

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

Arjun asked in Algorithms Apr 3

by Arjun

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2

qwer: 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: $\{1, 3, 5, 6, 7,8\}$ $\{2, 4, 9\}$ $\{2, 4\}$ $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$

Arjun asked in Algorithms Apr 3

by Arjun

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3

qwer: 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 $\{u,v,w,x\}$ $\{ \: \}$ $\{u,v,w,x,y,z\}$ $\{u,v,w\}$

Arjun asked in Algorithms Apr 3

by Arjun

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4

qwer: 4
The power set of the set $\{ \Phi \}$ is $\{ \Phi \}$ $\{ \Phi, \{ \Phi \} \}$ $\{ 0 \}$ $\{ 0, \Phi , \{ \Phi \} \}$

Arjun asked in Algorithms Apr 3

by Arjun

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5

qwer: 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: $B$ $A\cap \bar{B}$ $A - B$ $A\cap B$

Arjun asked in Algorithms Apr 3

by Arjun

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6

qwer: 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

Arjun asked in Algorithms Apr 3

by Arjun

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7

qwer: 7
Power set of empty set has exactly how many subset(s) One Two Zero Three

Arjun asked in Algorithms Apr 3

by Arjun

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8

qwer: 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 of some set (that is, there is some ... is a set and $|S| = 8$, then $S$ is not the power set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.

Arjun asked in Algorithms Apr 3

by Arjun

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9

qwer: 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 $3 \in A$. $A \cap B \supseteq\{2,3\}$ implies that $\{2,3\} \subseteq A$ and $\{2,3\} \subseteq B$. $A-B \supseteq\{3\}$ and $\{2\} \subseteq B$ implies that $\{2,3\} \subseteq A \cup B$.

Arjun asked in Algorithms Apr 3

by Arjun

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10

qwer: 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 $\{2,3,4\} \subseteq B$. $A-B \supseteq\{3,4\}$ ... $\{2,3\} \subseteq A \cup B$ implies that if $\{2,3\} \cap A=\emptyset$ then $\{2,3\} \subseteq B$.

Arjun asked in Algorithms Apr 3

by Arjun

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4 votes

1 answer

11

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 $\mathrm{W}(\mathrm{R})=n / 2$

GO Classes asked in Set Theory & Algebra Jan 28

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8 votes

1 answer

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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 $A \subseteq B$ $B \subseteq A$ $(B-A) \cup A=B$

GO Classes asked in Set Theory & Algebra Jan 13

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13

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

rajveer43 asked in Set Theory & Algebra Jan 11

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14

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

rajveer43 asked in Set Theory & Algebra Jan 10

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15

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

rajveer43 asked in Set Theory & Algebra Jan 10

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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

rajveer43 asked in Set Theory & Algebra Jan 10

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1 vote

1 answer

17

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

Rohit Chakraborty asked in Set Theory & Algebra Oct 6, 2023

by Rohit Chakraborty

408 views

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18

Discrete Mathematics | Set Theory | Equivalent Relation

Debargha Mitra Roy asked in Set Theory & Algebra Sep 23, 2023

by Debargha Mitra Roy

178 views

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19

Çșȇ ʛấẗẻ asked in Mathematical Logic Aug 28, 2023

by Çșȇ ʛấẗẻ

102 views

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