1. Union of Sets:- The union of two sets A and B, denoted A∪B, is the set containing all elements that are in A, B, or both. We write this mathematically as $A\cup B = \{x: x \varepsilon A, or, x \varepsilon B\}$.

2. Intersection of Sets:- The intersection of two sets A and B, denoted A∩B, is the set containing all elements that are in both A and B. We write this mathematically as $A\cap B = \{x: x \varepsilon A, and, x \varepsilon B\}$.

3. Relative compliment (Difference of Sets):- The difference of two sets A and B, denoted A− B or A∖B, is the set containing all elements that are in A but not in B. We write this mathematically as 𝐴 − 𝐵 = 𝐴\𝐵 $= \{x: x\varepsilon A \;and \;x\notin B\}$.

4. Absolute compliment (Compliment) : – Let 𝐴 be subset of a universal set 𝑈. The absolute complement (or simply complement) of set 𝐴, which is denoted by 𝐴′, is defined as the set of all elements of 𝑈 that are not in 𝐴. We write this mathematically as $𝐴 ′ = \{ x: x \in \cup \;and \;x \notin A \}$.

5. Symmetric Difference of Sets:- The symmetric difference of two sets A and B, denoted A△B, is the set containing all elements that are in either A or B but not in both. We write this mathematically as $A\Delta B = { x: x \in A/B \;or \; x \in B/A }$

6. Universal set:- A universal set (usually denoted by 𝑈) is a set which has elements of all the related sets, without any repetition of elements.

7. Cartesian product of Sets:- The Cartesian product of two sets A\ and B, denoted A×B, is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.

8. Equality of ordered pairs: – Equality of ordered pairs: If $(x, y) = (a, b)$, then, $x = a$ and $y = b$.

9. De Morgan’s Laws:- These laws relate the complement of the union and intersection of two sets:

1. $(A \cup B) ‘$  is equal to $A ‘ \cap B ‘ $
2. $(A \cap B) ‘$ is equal to $A ‘ \cup B ‘ $