Ordered Pairs

If $\left(4,y+2\right)=\left(a,7\right)$ then $a^2+y^2=$

For the following arrow diagram write the relation in the form of ordered pairs;

For the following arrow diagram write the relation in the form of ordered pairs;

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff xy>4$ such that $x\in A \& y\in B$.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff xy<3$ such that $x\in A \& y\in B$.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff xy>3$ such that $x\in A \& y\in B$.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff x+y>3$ such that $x\in A \& y\in B$.

$A=\left\{1,2\right\}$, $B=\left\{2,3\right\}$. Find binary relation $\left(x,y\right)\in R\iff x+y\le 3$ such that $x\in A \& y\in B$.

If $P=\left\{1, 2\right\}$ and $Q=\left\{3, 4\right\},$ then $P\times Q=\left\{\left(1, 3\right), \left(1, 4\right), \left(2, 3\right), \left(2, 4\right)\right\}.$

If the set $A$ has $p$ elements, $B$ has $q$ elements, then the number of elements in $A\times B$ is 

For the three sets $A, B \mathrm{and} C$, $A\times (B\cup C)=(A\times B)\cup (A\times C)$

Let $A$ be a set consisting of $10$ elements. The number of non-empty relations from $A$ to $A$ that are reflexive but not symmetric is

The number of ordered pairs $\left(a,b\right)$ of positive integers such that $\frac{2a-1}{b}$ and $\frac{2b-1}{a}$ are both integers is 

If $P=\{1,2,3)$ and $Q=\{1,4\}$ find sets $P\times Q$ and $Q\times P$.

 If $\left(x+\frac{1}{3},\frac{y}{3}-1\right)=\left(\frac{1}{2},\frac{3}{2}\right)$ find the values of $x$ and $y$.

If $A\times B=\left\{\left(1,2\right), \left(1,3\right), \left(1,6\right), \left(7,2\right), \left(7,3\right), \left(7,6\right)\right\}$, then find sets $A$ and $B$.

Let $A=\{x, y, z\}$ and $B=\{1, 2\}.$ If the number of relations from $A$ to $B$ is $k$, then find the value of $k$ where $k\in$ integer.

If $A=\{1,2\}$, $B=\{3,4\}$, then $A\times (B\cap \varnothing )=\varnothing$.

If $A$ and $B$ are non-empty sets, then $A\times B$ is a non-empty set of ordered pairs $(x,y)$ such that $x\in B$ and $y\in A$.

If $P=\{m,n\}$ and $Q=\{n,m\},$ then $P\times Q=\left\{\right(m,n),(n,m\left)\right\}$.