Relations Test ...

$$x^2=xy$$ is a relation which is:

The relation $$R=\{(1, 1), (2, 2), (3, 3)\}$$ on the set $$\{1, 2, 3\}$$ is

The minimum number of elements that must be added to the relation $$R =\{(1,2)(2,3)\}$$ on the set of natural numbers so that it is an equivalence is

Determine all ordered pairs that satisfy $$(x - y)^{2} + x^{2} = 25$$, where $$x$$ and $$y$$ are integers and $$x \geq 0$$. Find the number of different values of $$y$$ that occur

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

Let $$X$$ be the set of all persons living in a city. Persons $$x, y$$ in $$X$$ are said to be related as $$x < y$$ if $$y$$ is at least $$5$$ years older than $$x$$. Which one of the following is correct?

For any two real numbers $$\theta$$ $$\phi $$, we define $$\theta R \phi $$ if and only if $$\sec ^{ 2 }{ \theta  } -\tan ^{ 2 }{ \phi  } =1$$. The relation $$R$$ is

The relation $$R$$ defined on set $$A = \left \{x :|x| < 3, x\epsilon I\right \}$$ by $$R = \left \{(x, y) : y = |x|\right \}$$ is

Let the number of elements of the sets $$A$$ and $$B$$ be $$p$$ and $$q$$ respectively. Then the number of relations from the set $$A$$ to the set $$B$$ is

If $$N$$ denote the set of all natural numbers and $$R$$ be the relation on $$N\times N$$ defined by $$(a, b)R(c, d)$$. if $$ad(b + c) = bc (a + d)$$, then $$R$$ is