If $A, B$ and $C$ are any three sets, then $A \times (B \cup C)$ is equal to
$(A × B) \cup (A × C)$
$(A \cup B) × (A \cup C)$
$(A × B) \cap (A × C)$
None of these
Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that
$A \times C$ is a subset of $B \times D$
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
$(A \times B) \cap(A \times C)$
Let $A$ and $B$ be two sets such that $n(A)=3$ and $n(B)=2 .$ If $(x, 1),(y, 2),(z, 1)$ are in $A \times B$, find $A$ and $B$, where $x, y$ and $z$ are distinct elements.
If two sets $A$ and $B$ have $99$ elements in common, then the number of elements common to the sets $A \times B$ and $B \times A$ is equal to