a)

b)

c)

d)

2) Which among the following is the recursive definition of Factorial, i.e., n! ?

a)

b)

c)

b)

pedzenekO
2021-08-17
Answered

1) $110001$ binary number is equivalent to which of the following decimal number

a)$48$

b)$49$

c)$59$

d)$58$

2) Which among the following is the recursive definition of Factorial, i.e., n! ?

a)$f\left(0\right)=0,\text{}f\left(n\right)=\left(n\right)f(n-1),$ where $n\in Z$ and $n\ge 1$

b)$f\left(0\right)=1,\text{}f\left(n\right)=(n+1)f(n-1),$ where $n\in Z$ and $n\ge 1$

c)$f\left(0\right)=1,\text{}f\left(n\right)=\left(n\right)f(n-1),$ where $n\in Z$ and $n\ge 1$

b)$f\left(0\right)=0,\text{}f\left(n\right)=(n+1)f(n-1),$ where $n\in Z$ and $n\ge 1$

a)

b)

c)

d)

2) Which among the following is the recursive definition of Factorial, i.e., n! ?

a)

b)

c)

b)

You can still ask an expert for help

averes8

Answered 2021-08-18
Author has **92** answers

Step 1

Given

Step 2

Definition of Factorial is

If

So

Option

asked 2021-08-02

Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:$\cap \cup$

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:

asked 2021-07-28

Let A, B, and C be sets. Show that

asked 2021-08-18

Discrete Mathematics Basics

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where$(a,b)\in R$ if and only if

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

asked 2021-08-15

How many elements are in the set
{ 0, { { 0 } }?

asked 2022-07-15

Show that if $S1\subseteq S2$, then $\overline{{S}_{2}}\subseteq \overline{{S}_{1}}$ (the complement of S2 is the subset of the complement of S1)

asked 2022-05-27

Finding and drawing equivalence class with a binary set defined on RxR

In the question, it has been asked to find and draw the equivalence classes of the relation $\sim $ on $(\mathbb{R}\times \mathbb{R})\setminus \{(0,0)\}$ which is defined as

$({x}_{1},{x}_{2})\sim ({y}_{1},{y}_{2})\text{}\text{if}\text{}({y}_{1},{y}_{2})=\alpha ({x}_{1},{x}_{2})\text{, for some}\alpha \ne 0$

On solving, I have obtained the equivalence class as

$\begin{array}{rl}[(a,b)]& =\{(x,y)\in \mathbb{R}:(x,y)\sim (a,b)\}\\ & =\{(x,y)\in \mathbb{R}:(x,y)=\alpha (a,b)\}\end{array}$

On solving this, I got $x=\alpha a$ and $y=\alpha b$ and $x-y=\alpha (a-b)$ which will correspond to the set of straight lines having slope 1 and y-intercept $-\alpha (a-b)$ excluding the straight line passing.

But in the solution of this question, the equivalence class is given as the set of all straight lines passing through the origin(which is excluded).

I have just begun discrete math, and I am not getting any idea of the solution.

It would be really helpful if someone could help me with this.

In the question, it has been asked to find and draw the equivalence classes of the relation $\sim $ on $(\mathbb{R}\times \mathbb{R})\setminus \{(0,0)\}$ which is defined as

$({x}_{1},{x}_{2})\sim ({y}_{1},{y}_{2})\text{}\text{if}\text{}({y}_{1},{y}_{2})=\alpha ({x}_{1},{x}_{2})\text{, for some}\alpha \ne 0$

On solving, I have obtained the equivalence class as

$\begin{array}{rl}[(a,b)]& =\{(x,y)\in \mathbb{R}:(x,y)\sim (a,b)\}\\ & =\{(x,y)\in \mathbb{R}:(x,y)=\alpha (a,b)\}\end{array}$

On solving this, I got $x=\alpha a$ and $y=\alpha b$ and $x-y=\alpha (a-b)$ which will correspond to the set of straight lines having slope 1 and y-intercept $-\alpha (a-b)$ excluding the straight line passing.

But in the solution of this question, the equivalence class is given as the set of all straight lines passing through the origin(which is excluded).

I have just begun discrete math, and I am not getting any idea of the solution.

It would be really helpful if someone could help me with this.

asked 2022-07-17

There are three computers A, B, and C. Computer A has 10 tasks, Computer B has 15 tasks, and Computer C has 20 tasks. Each computer must complete its own tasks in order. After, each computer sends its output to a shared fourth computer. How many different orders can the outputs arrive at the fourth computer.