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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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Recent questions in Set Theory & Algebra

#541
735
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1 answers
1 votes
General Topic Doubt Set Theory & Algebra: Relations
How to check a relation is transitive or not from its matrix representation? Please help me with an example.
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#542
892
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1 answers
0 votes
Ace Test Series: Set Theory & Algebra - Relations
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________Ans given 48but I got 8Please verify
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#543
400
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1 answers
0 votes
Rosen,Ch:9,Ex:9.3,Q10
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#544
1.6k
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0 answers
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Lattice (ACE)
Let $A=\left \{ 1,2,3 \right \}$. A relation $R$ on $A\times A$ ... The poset $\left [ A\times A:R \right ]$ is a latticeAmong S1 and S2 which one is true?
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#545
1.7k
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1 answers
3 votes
kenneth rosen Ex2.4 Q.46
Show that the set of functions from the positive integers to the set {0,1,2,3,4,5,6,7,8,9} is uncountable.
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#546
509
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1 answers
0 votes
Kenneth Rosen Edition 6th Exercise 2.3 Question 36 (Page No. 147)
Let f be a function from the set A to the set B.Let S and T be subsets of A.Show that$f(S\cup T)=f(S)\cup f(T)$f(S\cap T)\subseteq f(S)\cap f(T)$Show that inclusion in part b can be proper
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#547
516
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1 answers
0 votes
kenneth rosen Ex 2.3 Q.29,30
Justify the statements.1. if f and f o g are one to one,does it follows that g is one to one.2 if f and f o g are onto,does it follow that g is onto
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#548
436
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0 answers
–1 votes
Kenneth Rosen Ex.2.3 Q.3(c)
https://prnt.sc/cncgcvplz explain the c part!
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#549
551
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0 answers
2 votes
JEST 2019
Let ${(0,1)}^n$ set of all binary string of length n. Hamming sphere of radius around a string C in ${(0,1)}^n$ is the set of all strings d$\epsilon$ ... S(C,k) and S(C',k) are disjointcouldn't remember rest of the options.
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#550
618
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0 answers
0 votes
JEST 2019 Descriptive Q3 (8 Marks)
Determine the number of functions f:{1,2,3…,n}→{1995,1996} satisfying the condition that f(1)+f(2)+…f(n) is odd.
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#551
592
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1 answers
1 votes
JEST Sample Question 1-a
Let a and b be positive integers such that a > b and a^ 2 − b^ 2 is a prime number.Then a^2 − b^ 2 is equal to(A) a − b(B) a + b(C) a × b(D) none of the above
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#552
920
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1 answers
3 votes
JEST Sample Question 1-b
When is the following statement true? (A ∪ B) ∩ C = A ∩ C(A) If Ā ∩ B ∩ C = φ(B) If A ∩ B ∩ C = φ(C) always(D) never
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#553
466
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1 answers
1 votes
Jest Exam sample question-3
How many subsets of even cardinality does an n-element set have ? Justify answer.Please give a proof if possible.This is part of subjective JEST paper.
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#554
18.0k
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9 answers
39 votes
GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$ ... $ and $R_2$R_1$ only$R_2$ onlyNeither $R_1$ nor $R_2$
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#555
348
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0 answers
0 votes
#math
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#556
12.9k
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5 answers
14 votes
GATE 2019
Let U = {1, 2, ..., n} and A = {(x, X), x ∈ X and X ⊆ U}. Consider the following twostatements for |A|.(i) |A| = n*$\small 2^{n-1}$(ii) |A|= Sigma(k= ... is correct?(a) (i) only (b) (ii) only(c) Both (i) and (ii) (d) None of the above
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#557
1.0k
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2 answers
0 votes
Gate 2019
What is the for the question where two statements were given as:S1: matrix A is invertibleS2:|A|=0?
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#558
418
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0 answers
0 votes
ME FLT5
Consider the following POSETs: Which of the above POSETs are isomorphic to (P (S), ⊆), where S = {a, b, c}?
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#559
1.3k
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1 answers
1 votes
MadeEasy Test Series 2019: Discrete Mathematics - Set Theory & Algebra
Which of the following are Well ordered set$\left [ Z^{+},\leq \right ]$\left [ Z^{-},\leq \right ]$\left [ Z^{+},\geq \right ]$\left [ Z^{-},\geq \right ]$
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#560
1.2k
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0 answers
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made easy test series
What is the number of generators in a group G, such that Ο(G) = 87?
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