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Syllabus: Sets, Relations, Functions, Partial orders, Lattices, Monoids, Groups.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&0& 1&0&1&0&0.83&1
\\\hline\textbf{2 Marks Count} &1&1&2& 0 &2&1&0&1.16&2
\\\hline\textbf{Total Marks} & 3&3&4&1&4&3&\bf{1}&\bf{3}&\bf{4}\\\hline
\end{array}}}$$

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Questions without a selected answer in Set Theory & Algebra

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Set Theory
Suppose A, B, and C are subsets of a universal set U. Also suppose that n(U) = 150 n(A) = n(B) = 2n(C) = 50, $A\cap B\cap C = ∅$ ... . How many elements are in at least two of the sets A, B, and C?
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141
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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 $g$ ... $f$ and $g$? Explain.
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133
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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 ... δ* (q, w) ∉ F] then ____________ A) R is ReflexiveB) R is SymmetricC) R is transitiveD) None
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139
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1 votes
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. ... addition is always associative) please let me know if iam correct.https://ibb.co/sPzHg6mhttps://ibb.co/sPzHg6m
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208
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1 answers
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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 ... that is also equal to equivalence class of the set on some equivalence relation.
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266
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1 answers
2 votes
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$
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267
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2 answers
1 votes
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?
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217
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1 answers
2 votes
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)\}$
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282
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3 answers
2 votes
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
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188
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1 answers
2 votes
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)$
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335
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1 answers
3 votes
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 \cup B|$|A-B|<|A \oplus B|<|A \cup B|<|A|+|B|$
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304
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1 answers
9 votes
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 ... )$((1,1), c,(0,0))$((1,1), a,(0,0))$((1,1), a,(1,1))$
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244
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1 answers
4 votes
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 ... $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.
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223
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0 answers
1 votes
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$
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280
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1 answers
4 votes
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$9$
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215
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1 answers
4 votes
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\}$
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253
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1 answers
4 votes
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\}$
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194
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1 answers
5 votes
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 \} \}$
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222
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1 answers
5 votes
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 $A$ ... (A - (A - B))$ is equal to:$B$A\cap \bar{B}$A - B$A\cap B$
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252
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2 answers
6 votes
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 $S_1 \cup S_2 \cup \dots \cup S_n = S$. Thenat least one of the sets $S_i$ is ... the sets $S_i$ can be finiteat least one of the sets $S_i$ is an infiniteNone of the above
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630
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3 answers
15 votes
GO Classes CS 2025 | Weekly Quiz 4 | Set Theory | Question: 7
Power set of empty set has exactly _______ subsets.OneTwoZeroThree
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725
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2 answers
23 votes
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 $T$ ... set of any set (that is, there is no set $T$ where $S = \mathcal{P}(T))$.
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276
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1 answers
7 votes
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 $2 \in A$ ... $\{2\} \subseteq B$ implies that $\{2,3\} \subseteq A \cup B$.
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157
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Question on Quotient set
What will be quotient set for equivalence relation R={(x,y) ∣ x ≡ y mod 5} in set builder form?
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3.1k
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2 answers
3 votes
GATE CSE 2024 | Set 2 | Question: 24
Let $\text{P}$ be the partial order defined on the set $\{1,2,3,4\}$ as follows\[P=\{(x, x) \mid x \in\{1,2,3,4\}\} \cup\{(1,2),(3,2),(3,4)\}\]The number of total orders on $\{1,2,3,4\}$ that contain $\text{P}$ is __________.
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2.8k
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2 answers
3 votes
GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
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2.2k
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2 answers
3 votes
GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the ... obeys the distributive lawOperator $\square$ over the operator $\diamond$ obeys the distributive law
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175
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0 answers
0 votes
#self doubt
Can someone please verify it ? isn't should be 8. https://www.toppr.com/ask/question/the-cardinality-of-the-power-set-of-left-phi-left-phiright-left-phi-left/Let S={ϕ,{ϕ},{ϕ,{ϕ}}}P(s)= Power ... ϕ}}},{{ϕ},{ϕ,{ϕ}}},{ϕ,{ϕ},{ϕ,{ϕ}}}}n(P(s))=6.
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635
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1 answers
5 votes
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 39
For sets $A$ and $B$, let $f: A \rightarrow B$ and $g: B \rightarrow A$ be functions such that $f(g(x))=x$ for each $x \in B$. Which among the ... function $f$ must be onto.The function g must be one-to-one.The function $g$ must be onto.
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