# Questions by Pooja Khatri

1 vote
1
How many 4 letter combinations can be made with the help of letters of the word STATISTICS?
2
Prove or disprove each of these statements about the floor and ceiling functions. $\left \lfloor \left \lceil x \right \rceil \right \rfloor = \left \lceil x \right \rceil$ for all real numbers $x.$ ... $x$ and $y.$
3
Prove or disprove each of these statements about the floor and ceiling functions. $\left \lceil \left \lfloor x \right \rfloor \right \rceil = \left \lfloor x \right \rfloor$ for all real number $x.$ $\left \lfloor 2x \right \rfloor = 2\left \lfloor x \right \rfloor$ whenever $x$ is a ... $x$ and $y.$ $\left \lceil x/2 \right \rceil = \left \lfloor x+1 / 2 \right \rfloor$ for all real numbers $x.$
4
Suppose that $f$ is a function from $A$ to $B$, where $A$ and $B$ are finite sets with $|A|=|B|$. Show that $f$ is one-to-one if and only if it is onto.
5
Let $S$ be a subset of a universal set $U$. The characteristic function $f_{s}$ of $S$ is the function from $U$ to the set $\left \{ 0,1 \right \}$ such that $f_{S}(x)=1$ if $x$ belongs to $S$ and $f_S(x)=0$ if $x$ does not belong to $S$. Let $A$ and $B$ be sets. Show that for all $x$ ... $f_{\sim A}= 1-f_{A} (x)$ $f_{A \oplus B}(x) = f_{A}(x) + f_{B}(x)- 2 f_{A}(x) f_{B}(x)$
6
Suppose that $f$ is an invertible function from $Y$ to $Z$ and $g$ is an invertible function from $X$ to $Y$. Show that the inverse of the composition $fog$ is given by $(fog)^{-1} = g^{-1} o f^{-1}.$
1 vote
7
Find the inverse function of $f(x) = x^3 +1.$
8
Draw graphs of each of these functions. $f(x) =$ $\left \lceil 3x-2 \right \rceil$ $f(x) =$ $\left \lceil 0.2x \right \rceil$ $f(x) =$ $\left \lfloor -1/x \right \rfloor$ $f(x) =$ $\left \lfloor x^2 \right \rfloor$ $f(x) =$ ... $f(x) =$ $\left \lfloor 2\left \lceil x/2 \right \rceil +1/2\right \rfloor$
9
Draw graphs of each of these functions. $f(x) =$ $\left \lfloor x+1/2 \right \rfloor$ $f(x) =$ $\left \lfloor 2x+1 \right \rfloor$ $f(x) =$ $\left \lceil x/3 \right \rceil$ $f(x) =$ $\left \lceil 1/x \right \rceil$ $f(x) =$ ... $\left \lfloor 2x \right \rfloor \left \lceil x/2 \right \rceil$ $f(x) =$ $\left \lceil \left \lfloor x-12 \right \rfloor + 1/2\right \rceil$
Draw the graph of the function $f(n) =$ $\left \lceil x \right \rceil +\left \lceil x/2 \right \rceil$ from $R$ to $R$
Draw the graph of the function $f(n) =$\left \lfloor x \right \rfloor +\left \lfloor x/2 \right \rfloor$from$R$to$R$0 votes 0 answers 12 Draw the graph of the function$f(n) =$\left \lfloor x/2 \right \rfloor$ from $R$ to $R$
Draw the graph of the function $f(n) =$\left \lfloor 2x \right \rfloor$from$R$to$R$0 votes 0 answers 14 Draw the graph of the function$f(n) = 1-n^2$from$Z$to$Z$0 votes 0 answers 15 Data are transmitted over a particular Ethernet network in blocks of$1500$octets (blocks of$8$bits). How many blocks are required to transmit the following amounts of data over this Ethernet network? (Note that a byte is a synonym for an octet, a kilobyte is$1000$bytes, and a ...$384\text{kilobytes}$of data$1.544\text{megabytes}$of data$45.3\text{megabytes of}$data 0 votes 0 answers 16 How many ATM cells (described in Example 28) can be transmitted in$10$seconds over a link operating at the following rates?$128$kilobits per second ($1$kilobit=$1000$bits)$300$kilobits per second$1$megabit per second ($1$megabit=$1,000,000$bits) 0 votes 0 answers 17 How many bytes are required to encode$n$bits of data where$n$equals$717100128800$1 vote 0 answers 18 How many bytes are required to encode$n$bits of data where$n$equals$4105003000$0 votes 0 answers 19 Let$a$and$b$be real numbers with$a<b$. Use the floor and / or ceiling functions to express the number of integers$n$that satisfy the inequality$a<n<b.$0 votes 0 answers 20 Let$a$and$b$be real numbers with$a<b$. Use the floor and / or ceiling functions to express the number of integers$n$that satisfy the inequality$a≤n≤b\$.