What is $9\mathrm{mod}3?$

Important Questions on Modular Arithmetic

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

A set $P=\{7, 21, 28, 42, 14, 0\}$ is given. A relation $R$ holds on elements $a$ and $b$ of set $P$ if either $a$ is a factor of $b$ or $b$ is a factor of $a\mathit{.}$ The relation $R$ on the set $P$ is

EASY

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

In the set $\mathrm{\mathbb{N}}$ of natural numbers, the relation $R=\left\{\left(x,y\right):x>y+5\right\}$ is

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

On $R$, a relation $\rho$ is defined by $x\rho y$ if and only if $x-y$ is zero or irrational. Then,

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

The relation $R$ defined in the set $\left\{1,2,3,4,5,6\right\}$ as $R=\left\{\left(a,b\right):b=a+1\right\}$ is

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $\rho$ be a relation defined on $N,$ the set of natural numbers, as $\rho =\left\{\right(x,y)\in N\times N:2x+y=41\}.$ Then

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let the relation $\rho$ be defined on $R$ by $a\rho b$ holds if and only if $a-b$ is zero or irrational, then

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

On the set $R$ of real numbers, the relation $\rho$ is defined by $x\rho y,(x,y)\in R$

EASY

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $R$ be a relation on the set $N$ be defined by $\mathrm{ }\left\{\left(x, y\right)| x, y\in N, 2x + y = 41\right\}$ . Then $R$ is

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $R$ be the relation on the set $R$ of all real numbers defined by $aRb$ if $|a-b|\le 1$, then $R$ is

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Pointing out to a lady, a girl said, "She is the daughter-in-law of the grandmother of my father's only son." How is the lady related to the girl ?

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $\rho$ be the relation on the set $R$ of all real numbers defined by setting a $\rho$ be if $\left|a-b\right| \le \frac{1}{2}$ .

HARD

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $S$ be the set of all real numbers. Then the relation $R=\left\{\left(a, b\right):1+ab>0\right\}$ on $S$ is

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $r$ be a relation from $R$ (set of real numbers) to $R$ defined by $r=\left\{\left(a, b\right)\right|a, b\in R$ and $a-b+\sqrt{3}$ is an irrational number}. The relation $r$ is

HARD

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Pointing to a photograph of a boy Suresh said, "He is the son of the only son of my mother." How is Suresh related to that boy?

EASY

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $R=\left\{\left(1\text{,}3\right)\text{,}\left(4\text{,}2\right)\text{,}\left(2\text{,}4\right)\text{,}\left(2\text{,}3\right)\text{,}\left(3\text{,}1\right)\right\}$ be a relation on the set  $A=\left\{1, 2, 3, 4\right\}$. The relation $R$ is

HARD

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let W denote the words in the English dictionary. Define the relation $R$ by : $R=\{\left(x,y\right)\in W\times W|$  the words $x$ and $y$ have at least one letter in common }.
Then $R$ is

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let a relation $R$ on the set $N$ of natural numbers be defined as $\left(x, y\right)\iff x^2-4xy+3y^2=0,\forall x, y\in N$. The relation $R$ is

MEDIUM

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $\mathrm{‘}A$ is disjoint from $B\mathrm{’}$ . Then $R$ is

EASY

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

For real numbers $x$ and $y$, we write $xRy\iff x-y+\sqrt{2}$ is an irrational number. Then the relation $R$ is

HARD

Mathematics>Arithmetic>Modular Arithmetic>Basics of Modular Arithmetic

Let $R$ be a relation over $N \times N$ and it is defined by $\left(a, b\right) R \left(c, d\right)⟺ a+d=b+c.$ Then $R$ is