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Recent questions tagged set-theory&algebra

25 votes
4 answers
872
GATE CSE 1989 | Question: 13c
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
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0 votes
0 answers
874
Equivalence relation
True / false ? a. Partitions formed from congruence classes modulo $6$ ... $R_4$ creates refinement partitions with respect to the partitions of $R_3$.
True / false ?a. Partitions formed from congruence classes modulo $6$ is a refinement of the partitions formed from congruence classes modulo 3s and t are bit strings and...
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0 votes
0 answers
875
GATE CSE 1988 | Question: 2iv
Give one property of the field of real numbers which no longer holds when we compute using finite-precision floating point numbers.
Give one property of the field of real numbers which no longer holds when we compute using finite-precision floating point numbers.
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20 votes
6 answers
876
GATE CSE 1988 | Question: 1vii
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
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43 votes
2 answers
877
GATE CSE 1989 | Question: 1-v
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given $n$) is ___________.
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given $n$) is ___________.
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21 votes
6 answers
878
GATE CSE 1989 | Question: 1-iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
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9 votes
2 answers
879
GATE CSE 1990 | Question: 17c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive prop...
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0 votes
1 answer
880
lattice
Theorem :- A lattice L is not a distributive lattice if and only if L has a sublattice which is isomorphic L1(kite structure) or L2(Pantagon structure). Anyone, please provide an example. I am not able to understand the theorem.
Theorem :- A lattice L is not a distributive lattice if and only if L has a sublattice which is isomorphic L1(kite structure) or L2(Pantagon structure).Anyone, please p...
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4 votes
2 answers
881
the number of generators of the group { 0,1,2........... 14} under the group operation addition modulu 15 is
the number of generators of the group { 0,1,2........... 14} under the group operation addition modulu 15 is
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21 votes
2 answers
882
GATE CSE 1990 | Question: 2-x
Match the pairs in the following questions: ...
Match the pairs in the following questions:$$\begin{array}{|ll|ll|}\hline (a) & \text{Groups} & (p) & \text{Associativity} \\\hline (b) & \text{Semigroups} & (q) & \text...
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25 votes
2 answers
884
GATE CSE 1987 | Question: 9e
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
How many true inclusion relations are there of the form $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
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23 votes
3 answers
885
GATE CSE 1987 | Question: 9b
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
How many one-to-one functions are there from a set $A$ with $n$ elements onto itself?
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24 votes
4 answers
886
GATE CSE 1987 | Question: 9a
How many binary relations are there on a set $A$ with $n$ elements?
How many binary relations are there on a set $A$ with $n$ elements?
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22 votes
4 answers
887
GATE CSE 1987 | Question: 2d
State whether the following statements are TRUE or FALSE: The union of two equivalence relations is also an equivalence relation.
State whether the following statements are TRUE or FALSE:The union of two equivalence relations is also an equivalence relation.
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1 votes
2 answers
889
set theory
What is the number of relations which are either symmetric or antisymmetric on a set with 3 elements?
What is the number of relations which are either symmetric or antisymmetric on a set with 3 elements?
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0 votes
1 answer
890
General Topic Doubt Set Theory & Algebra: Groups
In the above question my doubt is instead of under multiplication if we change under ADDITION then what is its value?plz someone explain details.
In the above question my doubt is instead of under multiplication if we change under ADDITION then what is its value?plz someone explain details.
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8 votes
1 answer
892
Groups theory
Let $G:$ be a group. $a^5=e,\quad aba^{-1}=b^2,\quad a,b,\in G$ Then which of the following is an order of $b$? $31$ $32$ $30$ $2$
Let $G:$ be a group.$a^5=e,\quad aba^{-1}=b^2,\quad a,b,\in G$Then which of the following is an order of $b$?$31$$32$$30$$2$
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2 votes
2 answers
893
How to determine whether the grammar is regular or not?
If any grammer is given, how can we tell that the grammar is regular or not? Is that any perticular method?
If any grammer is given, how can we tell that the grammar is regular or not? Is that any perticular method?
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4 votes
2 answers
895
UGC NET CSE | June 2016 | Part 2 | Question: 1
How many difference equivalence relations with exactly three different equivalence classes are there on a set with five elements? 10 15 25 30
How many difference equivalence relations with exactly three different equivalence classes are there on a set with five elements?10152530
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3 votes
1 answer
896
RELATIONS
Suppose that A is a nonempty set, and f is a function that has A as its domain. Let R be the relation on A consisting of all ordered pairs (x, y) such that f (x) = f (y). What are the equivalence classes of R?
Suppose that A is a nonempty set, and f is a function that has A as its domain. Let R be the relation on A consisting of all ordered pairs (x, y) such that f (x) = f (y)....
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0 votes
2 answers
897
GATE Overflow | Mathematics | Test 1 | Question: 13
For a function to be invertible it has to be one to one onto both one to one and onto none
For a function to be invertible it has to beone to one onto both one to one and ontonone
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1 votes
2 answers
899
GATE Overflow | Mathematics | Test 1 | Question: 1
A relation $R$ is defined as $xRy$ , if $x$ and $y$ are NOT equal. This relation $R$ is symmetric but not reflexive symmetric and transitive but not reflexive an equivalent relation none of reflexive or symmetric or transitive
A relation $R$ is defined as $xRy$ , if $x$ and $y$ are NOT equal. This relation $R$ issymmetric but not reflexivesymmetric and transitive but not reflexivean equivalent ...
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