Recent questions and answers in Set Theory & Algebra - GATE CSE Doubts

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Gate 2016 Set Theory
Consider a set U of 23 different compounds in a chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements: Each compound in U \ S reacts with an odd number of compounds ... Which one of the above statements is ALWAYS TRUE? (Please Draw a graph Not Able to visualize) Only I Only II Only III None.

asked Apr 3 in Set Theory & Algebra by sushildiwakar (5 points) | 5 views

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#self-doubt #Group-theory
let S be a semigroup over an operation *, having p,q,e as it’s elements, such that p*e=p; q*e=q; e*e=e and also p*q=p. Then will this semi group be a monoid?

asked Mar 28 in Set Theory & Algebra by Shar_10 (5 points) | 9 views

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TIFR-GS2021 Question
Fix $n\geq6$. Consider the set $C$ of binary strings $x_1x_2...x_n$ of length n such that the bits satisfy the following set of equalities, all modulo 2: $x_i + x_{i+1} + x_i+2 = 0$ for all $1\leq i\leq n-2, x_{n-1} + x_n + x_1 = 0$, and $x_n + x_1 + x_2 = 0$. What ... $n \geq6$ is divisible by $3$ then $|C| = 4$. If $n\geq 6$ is not divisible by $3$ the $|C| =14$

asked Mar 24 in Set Theory & Algebra by zxy123 (3.6k points) | 6 views

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Made easy test series Discrete Mathematics-2
The number of ways of splitting a set of n elements into two parts is Answer is $2^{n-1} – 1$, explanation states this is because partitions can’t be empty, is this true?

asked Jan 29 in Set Theory & Algebra by zxy123 (3.6k points) | 39 views

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Lattice self doubt
Establish relationship between semi lattice, lattice, bounded lattice, finite lattice, complement lattice, distribute lattice and Boolean algebra. [ Using Venn Diagram ]

asked Jan 18 in Set Theory & Algebra by tusharSingh (5 points) | 7 views

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how to prove function injective or not
Let A, B, and C be finite sets, and f : B to C and g : A to B be functions. Let h be the function with domain A and range C that maps x in A to f (g(x)). Prove or disprove the following claim: If h is injective, then g must be injective.

asked Dec 21, 2020 in Set Theory & Algebra by tyagiabhi (5 points) | 20 views

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#self-doubt #discrete-maths
can someone explains difference between equivalence classes and partitions. according to wiki Every element x of X is a member of the equivalence class [x]. Every two equivalence classes [x] and [y] are either equal or disjoint. ... below gate question https://gateoverflow.in/652/gate2000-2-5 they considers equivalence classes as partitions.Can someone explains why?

answered Dec 2, 2020 in Set Theory & Algebra by zxy123 (3.6k points) | 19 views

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#dicrete-maths #made-easy
Let G be a group.Suppose that the number of elements in G of order 5 is 28.Determine the number of distinct subgroups of G of order 5 __. Ans -7 .can someone explains how?

answered Nov 28, 2020 in Set Theory & Algebra by zxy123 (3.6k points) | 18 views

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#discrete-maths #made-easy
In a poset (A,<=) ,if there is no element ,x belongs to A with x<y then which of the following is true? An element x exists for which x=y. An element x is maximal in poset. A set with the same subset of poset An element x is ... correct bcz an element x is said to maximal if there exists no element y belongs to A such that xRy holds (x<y in this question).

asked Nov 28, 2020 in Set Theory & Algebra by 404 found (37 points) | 10 views

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#discrete-maths #made-easy
For sets A and B ,let f:A?B and g:B?A be functions such that f(g(x))=x for each x.which of the following options is/are true? The function f must be one to one. The function f must be onto The function g must be one to one the function g must be onto ans is b,c. can someone explains how?

asked Nov 28, 2020 in Set Theory & Algebra by 404 found (37 points) | 12 views

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Zeal testseries
Are the ordered pairs ($\phi$,$\phi$) , (1,$\phi$) possible?

answered Nov 26, 2020 in Set Theory & Algebra by zxy123 (3.6k points) | 15 views

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Zeal testseries
What will be S :- S=$\phi$ or S={$\phi$} and what will be the cardinality of S :- 1 or 2?

answered Nov 26, 2020 in Set Theory & Algebra by zxy123 (3.6k points) | 18 views

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Zeal test series
Wat will be the value of p :- 1 or 0?

asked Nov 25, 2020 in Set Theory & Algebra by Kindaichi (10 points) | 23 views

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Kenneth h rosen 7th Edition chapter 2 section 2.5 "cardinality of sets"

answered Nov 21, 2020 in Set Theory & Algebra by ijnuhb (747 points) | 27 views

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Kenneth h rosen 7th Edition chapter 2 section 2.4 "Sequences and Summation"

asked Nov 20, 2020 in Set Theory & Algebra by ykrishnay (7 points) | 23 views

+1 vote

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question from site yutsumura
Let G be a group. Suppose that the number of elements in G of order 5 is 28. Determine the number of distinct subgroups of G of order 5. source of ques – https://yutsumura.com/if-there-are-28-elements-of-order-5-how-many-subgroups-of-order-5/ I didn’t understand the solution given over there … Can anyone please solve this ….

answered Nov 6, 2020 in Set Theory & Algebra by zxy123 (3.6k points) | 154 views

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Finding the transitive closure by using Warshall Algorithm

asked Nov 1, 2020 in Set Theory & Algebra by Moon_99 (5 points) | 27 views

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ACE handbook
Suppose that S is a set with n elements. How many ordered pairs (A , B) are there such that A and B are subsets of S and A is subset of B? 1. 2^n 2. 3^n 3.n^2 4.C(n , 2)

answered Oct 17, 2020 in Set Theory & Algebra by mayureshpatle (861 points) | 53 views

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Gatebook function
How to solve this type of question ?

asked Oct 2, 2020 in Set Theory & Algebra by Raj_81 (23 points) | 23 views

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UGC NET 2016 as well as Discrete Maths Kenneth Rosen PAGE Pg 657 Q21 [closed]

asked Sep 15, 2020 in Set Theory & Algebra by ijnuhb (747 points) | 25 views

+1 vote

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#Self_Doubt #Set-theory #GATECSE2015
Suppose L={p,q,r,s,t}L={p,q,r,s,t} is a lattice represented by the following Hasse diagram: For any x,y∈Lx,y∈L, not necessarily distinct , x∨y and x∧y are join and meet of x,y respectively. Let L3={(x,y,z):x,y,z∈L} be the set of all ordered ... )∧(x∨z) for L1* and L2* respectively. Then (A) P1>P2 (B) P1<P2 (C) P1=P2 (D) none which one should be correct?

answered Aug 27, 2020 in Set Theory & Algebra by suvradip das (119 points) | 73 views

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DU MCA Entrance 2017
If A is a 3*3 Matrix with Eigenvalues 2 and -1 and the respective Eigenvectors (1 2 0) and (0 0 1), then the vectors A^3 (1 2 2) is equal to ; ( 8 16 6) (2 4 -2) (8 16 -1) (8 16 -2)

asked Aug 25, 2020 in Set Theory & Algebra by Jatin99 (5 points) | 17 views

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LATTICE ASSOCIATIVITY DOUBT
I wasn't convinced about the associativity property of lattices, and the proof i found on math.stackexchange seemed reasonable, but still i couldnt wrap my head around it. I tried to make a counter example, and in the above diagram (b join c) ... otherwise it would've satisfied associativity. But i cant seem to figure out why this diagram isn't a lattice. Please help.

answered Aug 25, 2020 in Set Theory & Algebra by varsha394 (11 points) | 64 views

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ISI CSB 2018
State, with justification, which of the following expressions f, g and h, define valid real-valued functions over the set of positive rational numbers. We denote a rational number by m/n, where m and n are positive integers. (a) f(m/n) = 2^m − 2^n. (b) g(m/n) = log m − log n. (c) h(m/n) = (m^2 − n^2)/(mn).

answered Aug 20, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 32 views

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Kenneth rosen (7th edition) chapter 9
Let (S,R) be a poset.show that(S,$R^{-1}$) is also a poset.where $R^{-1}$ is the inverse of R.explain with example.

answered Aug 16, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 20 views

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Self problems
Lim x-->0 [ (cosx - cos(sinx))/x^4 ]= ?? Please!! tell me the best approach to solve this question

answered Aug 16, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 48 views

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Kenneth Rosen 9.5 Exercise 15
Let R be the relation on the set of ordered pairs of positive integers such that ((a,b),(c,d)) ∈ R if and only if a+d = b+c. Show that R is an equivalence relation.

answered Aug 16, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 45 views

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2 answers

Group Theory Book
Any standard book for group theory numericals?

answered Aug 16, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 98 views

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#self doubt Function
Whether gof is one -one for the picture given below?

answered Aug 16, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 19 views

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Discrete Maths
What if I have a function "X" and it's inverse "Y" can I guaranteed say that the function X is bijective? Or in simple terms can I say inverse of a function exists if and only if it's bijective?

answered Aug 15, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 34 views

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#disctete math function
Q.Let f(x) be a polynomial and g(x)=f'(x) be its derivatives . if the degree of (f(x)+f(-x)) is 10, then degree of (g(x)+g(-x)) is_________.

answered Aug 15, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 17 views

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Show that given relation is an equivalence relation?

answered Aug 15, 2020 in Set Theory & Algebra by jayeshasawa001 (2.5k points) | 63 views

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Self doubt on relations and functions
Is x^3 injective or not in interval of all integers i.e. form - infinity to +infinity?Please explain.

answered Aug 15, 2020 in Set Theory & Algebra by jayeshasawa001 (2.5k points) | 27 views

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1 answer

Is rings and fields in gate syllabus?

answered Aug 15, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 88 views

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madeeasy set theory
What is the meaning of symmetric relations are closed under complementation ..?Please cite an example..

answered Aug 12, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 37 views

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Self doubt: Ordered Pair
What is meaning of ordered pair of rational numbers, or ordered pair of integers , or real numbers??

answered Aug 12, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 56 views

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1 answer

Mathematics ME Test series
Ques:- What is the number of partition of X = {a, b, c, d, e, f} where a and c are always in same block? - 15 - 52 - 203 - None of these

answered Aug 12, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 56 views

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1 answer

Relation :DiscreteMath-GB
Let R be a relation from a set A to a set B. The inverse relation from B to A, denoted by , is the set of ordered pairs . S1: R is reflexive relation iff S2: R is a symmetric relation iff Which one of the following statements is true? (A).Only S1 (B).Only S2 (C).Both S1 and S2 (D).None

answered Aug 11, 2020 in Set Theory & Algebra by Arkaprava (801 points) | 72 views

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ISI CSB 2018
Given A = {1, 2, 3, .... , 70}, show that for any six elements a1, a2, a3, a4, a5 and a6 belonging to A, there exists one pair ai and aj for which |ai − aj| ≤ 14 (i not equals to j).

answered Aug 11, 2020 in Set Theory & Algebra by toxicdesire (555 points) | 34 views

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Discrete Mathematics-Functions
Let $A=\{1,2,3,4,5\},B=\{w,x,y,z\},A_{1}=\{2,3,5\}\subseteq A$ and $g:A_{1}\rightarrow B.$ In how many ways can $g$ be extended to a function $f:A\rightarrow B$

asked Jul 25, 2020 in Set Theory & Algebra by KUSHAGRA गुप्ता (1.4k points) | 45 views

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