Hey Developer’s, I’m back with a new topic which is Set Operations On Events in the series of statistics foundations.

### Quick Referesher

**Simple Event** : It cannot be decomposed. Ex: Player Rolled a 6

**Complex Event :** It can be decomposed into simpler events. Ex: Player rolled a even number can be decomposd into player rolled a 2,4 or 6.

So, let’s get started …

### Set Union

A union of two sets A and B is basically a set that contains all the elements from A and B, and the common elements do not repeat.

Ex: if A = {1,2,3} and B = {1,x,∞} then A ⋃ B = {1,2,3,x,∞}

### Set Intersection

An intersection of two sets A and B is a set containing all that belong to both A and B.

Basically the common elements from both the sets.

Ex: if A = {1,2,3} and B = {1,x,∞} then A ⋂ B = {1}

### Set Difference

The relative complement or **set difference** of **sets** A and B denoted **A – B**, is the **set** of all elements in A that are not in B.

Ex: If A = {1,2,3} and B = {3,4,5} then A – B = {1,2}

### Set Operations On Events

Suppose a die roll is, S = {E1,E2,E3,E4,E5,E6}

An even roll is ,S(even) = {E2,E4,E6}

An roll that is greater than 3, S>3 = {E4,E5,E6}

A roll that is even **or** greater than 3, S(even) ∪ S>3 = {E2,E4,E5,E6}

A roll that is even **and** greater than 3, S(even) ∩ S>3 = {E4,E6}

A roll that is odd** and** greater than 5,S(odd) ∩ S>5 = ∅

#### Next Post will be on Independence Of Events

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