If $G =\{7,8\}$ and $H =\{5,4,2\},$ find $G \times H$ and $H \times G$.
$G =\{7,8\}$ and $H =\{5,4,2\}$
We know that the Cartesian product $P \times Q$ of two non-empty sets $P$ and $Q$ is defined as
$P \times Q-\{(p, q): p \in P, q \in Q\}$
$\therefore G \times H=\{(7,5),(7,4),(7,2),(8,5),(8,4),(8,2)\}$
$H \times G=\{(5,7),(5,8),(4,7),(4,8),(2,7),(2,8)\}$
If $A \times B =\{(p, q),(p, r),(m, q),(m, r)\},$ find $A$ and $B$
State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
If $A=\{1,2\}, B=\{3,4\},$ then $A \times\{B \cap \varnothing\}=\varnothing$
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 $A=\{-1,1\},$ find $A \times A \times A.$
If $A, B$ and $C$ are any three sets, then $A \times (B \cup C)$ is equal to