### Theory:

Finite set: A set that has a finite number of elements is called finite set.
Example:
• The set of positive integers less than $$50$$.
• The set of prime factors of $$275$$.
• The set of vowels in alphabets.
• The set of keys on the laptop.
Infinite set: A set that has an infinite number of elements is called an infinite set.
Example:
• The set of rational numbers.
• The set of powers of $$2$$.
• The set of multiples of $$6$$.
• The collection of all even integers.
Set notation: A set is denoted by capital letters English alphabets $$A, B, C, D,...$$
Elements: Elements of the sets are denoted by small letters English alphabets $$a, b, c,...$$
Also, elements of the set should be written inside the curly brackets $\left\{\right\}$.
Important!
Suppose the element $$x$$ lies in the set $$A$$, then we can say that as $$x$$ belongs to the set $$A$$. That is, $$x$$$\in$$$A$$.

Suppose the element $$x$$ doesn't lie in the set $$A$$, then we can say that $$x$$ does not belong to the set $$A$$. That is, $$x$$$\notin$ $$A$$.
Example:
Consider the set $A\phantom{\rule{0.147em}{0ex}}=\left\{2,\phantom{\rule{0.147em}{0ex}}4,\phantom{\rule{0.147em}{0ex}}6,\phantom{\rule{0.147em}{0ex}}8,\phantom{\rule{0.147em}{0ex}}10\right\}$.

Here $$2$$ is an element of $$A$$. That is $2\in A$.

$$4$$ is an element of $$A$$. That is $4\in A$.

$$6$$ is an element of $$A$$. That is $6\in A$.

$$8$$ is an element of $$A$$. That is $8\in A$.

$$10$$ is an element of $$A$$. That is $10\in A$.

But the element $$5$$ doesn't belong to $$A$$. That is $5\notin A$.