Cartesian Products of Sets

Let $A=\left\{1, 2, 3\right\}, B=\left\{3, 4\right\}$ and $C=\left\{4, 5, 6\right\}$. Find $\left(A\times B\right)\cup \left(A\times C\right)$.

Let $A=\left\{1, 2, 3\right\}, B=\left\{3, 4\right\}$ and $C=\left\{4, 5, 6\right\}$. Find $A\times \left(B\cup C\right)$.

Let $A=\left\{1, 2, 3\right\}, B=\left\{3, 4\right\}$ and $C=\left\{4, 5, 6\right\}$. Find $\left(A\times B\right)\cap \left(A\times C\right)$.

If $P=\left\{1,3,4,5,7,9,10,12\right\}, Q=\left\{2,4,5,6,9,11,12,14,15\right\}$ then $\frac{2\times n\left(\left(P\times Q\right)\times Q\right)}{n\left(\left(P\times Q\right)\cap \left(Q\times P\right)\right)}=?$

For sets $A$ and $B$, $n\left(A\right)=3$ and $n\left(A\times \left(B-A\right)\right)=6$, then $n\left(B\right)$ cannot be

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

If $A=\left\{a,b,c\right\}$, $B=\left\{x,y\right\}$, then write $A\times B.$

Suppose that the number of elements in set $A$ is $p$, the number of elements in set $B$ is $q$ and the number of elements in $A\times B$ is $7,$ then $p^2+q^2=$

Consider the sets $A=\left\{1,2,3\right\}$, $B=\left\{a,b,c\right\}$. Write $n\left(A\times B\right)$.

Consider the sets $A=\left\{1,2,3\right\}$, $B=\left\{a,b,c\right\}$. Find $A\times B$.

If $A\times B=\left\{\left(p, q\right), \left(p, r\right), \left(m, q\right), \left(m, r\right)\right\}$, find $A$ and $B$.

If $R$ is the set of all real numbers, what do the cartesian products $R\times R$ and $R\times R\times R$ represent?

If $P=\left\{1, 2\right\}$, form the set $P\times P\times P$.

Let $A=\left\{1, 2, 3\right\}, B=\left\{3, 4\right\}$ and $C=\left\{4, 5, 6\right\}$. Find $A\times \left(B\cap C\right)$.

If $P=\left\{a, b, c\right\}$ and $Q=\left\{r\right\}$, form the sets $P\times Q$ and $Q\times P$. Are these two products equal?

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

If $P=\left\{n,i,s,e,r\right\},Q=\left\{n,e,s,t\right\}$ and $R=\left\{c,e,b,s\right\}$, then the number of elements in $\left(P\cup Q\right)\times R$ is

Check whether the Cartesian product of sets is Associative or not For the sets given below.

$A=\left\{a,b\right\}, B=\left\{c,d\right\}, C=\left\{e,f\right\}$

$A,B,C$ are some finite sets

$A\times \left(B-C\right)=$

If $A=\left\{2\right\}$ and $B=\left\{3,5\right\}$, then verify that $A\times B\ne B\times A$.