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Recent questions tagged set-theory&algebra

55 votes
6 answers
1113
GATE CSE 1997 | Question: 6.3
The number of equivalence relations of the set $\{1,2,3,4\}$ is $15$ $16$ $24$ $4$
The number of equivalence relations of the set $\{1,2,3,4\}$ is$15$$16$$24$$4$
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27 votes
4 answers
1115
GATE CSE 1997 | Question: 4.4
A polynomial $p(x)$ is such that $p(0) = 5, p(1) = 4, p(2) = 9$ and $p(3) = 20$. The minimum degree it should have is $1$ $2$ $3$ $4$
A polynomial $p(x)$ is such that $p(0) = 5, p(1) = 4, p(2) = 9$ and $p(3) = 20$. The minimum degree it should have is$1$$2$$3$$4$
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24 votes
4 answers
1116
GATE CSE 1997 | Question: 3.3
In the lattice defined by the Hasse diagram given in following figure, how many complements does the element ‘$e$’ have? $2$ $3$ $0$ $1$
In the lattice defined by the Hasse diagram given in following figure, how many complements does the element ‘$e$’ have?$2$$3$$0$$1$
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41 votes
2 answers
1120
GATE CSE 2014 Set 3 | Question: 3
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________.
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________....
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25 votes
3 answers
1123
GATE CSE 2014 Set 2 | Question: 49
The number of distinct positive integral factors of $2014$ is _____________
The number of distinct positive integral factors of $2014$ is _____________
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30 votes
3 answers
1124
GATE CSE 2014 Set 2 | Question: 5
A non-zero polynomial $f(x)$ of degree 3 has roots at $x=1$, $x=2$ and $x=3$. Which one of the following must be TRUE? $f(0)f(4)< 0$ $f(0)f(4)> 0$ $f(0)+f(4)> 0$ $f(0)+f(4)< 0$
A non-zero polynomial $f(x)$ of degree 3 has roots at $x=1$, $x=2$ and $x=3$. Which one of the following must be TRUE? $f(0)f(4)< 0$$f(0)f(4) 0$$f(0)+f(4) 0$$f(0)+f(4)< 0...
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60 votes
6 answers
1125
GATE CSE 2014 Set 1 | Question: 50
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is...
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41 votes
5 answers
1126
GATE CSE 2012 | Question: 37
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set? $ 2^{n}$ $2^{n} – 1$ $2^{n} – 2$ $2(2^{n} – 2)$
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set?$ 2^{n}$$2^{n} – 1$$2^{n} – 2$$2(2^{n} – 2)$
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32 votes
3 answers
1127
GATE CSE 1998 | Question: 12
Let $(A, *)$ be a semigroup, Furthermore, for every $a$ and $b$ in $A$, if $a \neq b$, then $a*b \neq b*a$. Show that for every $a$ in $A$, $a*a=a$ Show that for every $a$, $b$ in $A$, $a*b*a=a$ Show that for every $a,b,c$ in $A$, $a*b*c=a*c$
Let $(A, *)$ be a semigroup, Furthermore, for every $a$ and $b$ in $A$, if $a \neq b$, then $a*b \neq b*a$.Show that for every $a$ in $A$, $a*a=a$Show that for every $a$,...
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20 votes
6 answers
1129
GATE CSE 1998 | Question: 10a
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$
Prove by induction that the expression for the number of diagonals in a polygon of $n$ sides is $\frac{n(n-3)}{2}$
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20 votes
4 answers
1132
GATE CSE 1998 | Question: 1.8
The number of functions from an $m$ element set to an $n$ element set is $m + n$ $m^n$ $n^m$ $m*n$
The number of functions from an $m$ element set to an $n$ element set is$m + n$$m^n$$n^m$$m*n$
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19 votes
5 answers
1134
GATE CSE 1998 | Question: 1.6
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is $n$ $n^2$ $1$ $n+1$
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is$n$$n^2$$1$$n+1$
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23 votes
2 answers
1138
GATE CSE 1999 | Question: 1.2
The number of binary relations on a set with $n$ elements is: $n^2$ $2^n$ $2^{n^2}$ None of the above
The number of binary relations on a set with $n$ elements is:$n^2$$2^n$$2^{n^2}$None of the above
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36 votes
6 answers
1139
GATE CSE 2005 | Question: 7
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be:$O(n)$$O(n \log n)$$O \left( n^{\frac{3}{2}} \right)...
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