Set theory

1. Set

2. Equal set

3. Subset

4.

• For every set, $\varnothing \subseteq S$ and $S\subseteq S$ theorem

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5. Cardinality

6. A set can be Infinite

7. Power sets

8. Ordered tuples: $(a_1,a_2)$

9. Cartesian product:

10. Cartesian product for multiple set:

11. Set union

12. Set intersection

13. Set difference

14. Complement operation:

• $\overline{S}=\{x|x\in U,x\notin S\}=U-S$

15. $S=(S\cap T)\cup (S-T)$ for all set of S and Ttheorem

16. Strings:

17. Russell’s paradox

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