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6 votes
41
GATE CSE 2006 | Question: 2
Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is $z^{2^{xy}}$ $z \times 2^{xy}$ $z^{2^{x+y}}$ $2^{xyz}$
Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is$z^{2^{...
33 votes
42
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.
23 votes
47
GATE CSE 2007 | Question: 3
What is the maximum number of different Boolean functions involving $n$ Boolean variables? $n^2$ $2^n$ $2^{2^n}$ $2^{n^2}$
What is the maximum number of different Boolean functions involving $n$ Boolean variables?$n^2$$2^n$$2^{2^n}$$2^{n^2}$
0 votes
49
GATE CSE 2015 Set 1 | Question: 5
If $g(x) = 1 - x$ and $h(x) = \frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is: $\frac{h(x)}{g(x)}$ $\frac{-1}{x}$ $\frac{g(x)}{h(x)}$ $\frac{x}{(1-x)^{2}}$
If $g(x) = 1 - x$ and $h(x) = \frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is:$\frac{h(x)}{g(x)}$$\frac{-1}{x}$$\frac{g(x)}{h(x)}$$\frac{x}{(1-x)^{2}}$
6 votes
50
GATE CSE 2015 Set 1 | Question: 28
The binary operator $\neq$ ... about the binary operator $\neq$ ? Both commutative and associative Commutative but not associative Not commutative but associative Neither commutative nor associative
The binary operator $\neq$ is defined by the following truth table.$$\begin{array}{|l|l|l|} \hline \textbf{p} & \textbf{q}& \textbf{p} \neq \textbf{q}\\\hline \text{0} & ...
–3 votes
51
GATE CSE 1996 | Question: 1.2
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is $3$ $4$ $9$ None of the above
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is$3$$4$$9$No...
14 votes
53
GATE CSE 1991 | Question: 01,xiv
If the longest chain in a partial order is of length $n$, then the partial order can be written as a _____ of $n$ antichains.
If the longest chain in a partial order is of length $n$, then the partial order can be written as a _____ of $n$ antichains.
4 votes
56
GATE CSE 1998 | Question: 1.6
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is $n$ $n^2$ $1$ $n+1$
Suppose $A$ is a finite set with $n$ elements. The number of elements in the largest equivalence relation of A is$n$$n^2$$1$$n+1$
6 votes
62
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)...
6 votes
63
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 $\frac{n(n-3)}{2}$
6 votes
64
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.
18 votes
65
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?
13 votes
67
GATE CSE 2007 | Question: 2
Let $S$ be a set of $n$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $S$ are: $n$ and $n$ $n^2$ and $n$ $n^2$ and $0$ $n$ and $1$
Let $S$ be a set of $n$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $S$ are:$n$ and $n$$n^2$ and $n$$n^2$ and $0$$n$ an...
1 votes
69
TIFR CSE 2010 | Part A | Question: 18
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ? $2^{n+1}$ $2^{2n}$ $3^{n}$ $2^{n} + 1$ $3^{n + 1}$
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ?$2^{n+1}$$2^{2n}$$3^{n}$$2^{n} + 1$$3^{n + 1}...
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