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 the set $A$ has $3$ elements and the set $B=\{3,4,5\},$ then find the number of elements in $( A \times B ).$
State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly.
If $P=\{m, n\}$ and $Q=\{n, m\},$ then $P \times Q=\{(m, n),(n, m)\}.$
$A = \{1,2,3,4......100\}, B = \{51,52,53,...,180\}$, then number of elements in $(A \times B) \cap (B \times A)$ is
If $\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right),$ find the values of $x$ and $y$
Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find
$A \times(B \cup C)$