Two sets $A$ and $B$ are as under:
$A = \{(a, b) \in R \times R : |a - 5| < 1$ and $|b - 5| < 1\} $;
$B = \{(a, b) \in R \times R : 4(a - 6)2 + 9(b - 5)^2 \leq 36\}$. Then
As, $|a-5|<1$ and $|b-5|<1$$\Rightarrow 4< a , b <6$ and $\frac{(a-6)^{2}}{9}+\frac{(b-5)^{2}}{4} \leq 1$
Taking axes as $a$-axis and $b$-axis
The set $A$ represents square $PQRS$ inside set $B$ representing ellipse and hence $A \subset B$.
Empty Set - It is a set that has no element in it. It is also called a null or void set and is denoted by Φ or {}.
Singleton Set - It is a set that contains only one element.
Finite Set - A set that has a finite number of elements in it.
Infinite Set - A set that has an infinite number of elements in it.
Equal Set - Sets in which elements of one set are similar to elements of another set. The sequence of elements can be any but the same elements exist in both sets.
Sub Set - Set X will be a subset of Y if all the elements of set X are the same as the element of set Y.
Power Set - It is the collection of all subsets of a set X.
Universal Set - A basic set that has all the elements of other sets and forms the base for all other sets.
Disjoint Set - If there is no common element between two sets, i.e if there is no element of Set A present in Set B and vice versa, then they are called disjoint sets.
Overlapping Set - It is the set of two sets that have at least one common element, called overlapping sets.
