Sets - Mathematical Foundations

Explain:

Initial definitions of: Sets, Elements, Subsets

1A Sets:

$$A=\{1,2,3,4,5\}$$ $$B=\{1,3,5\}$$

C = { 2,4,6 }

$$A\ast set\ast issimplyacollectionofdifferentthingswithinthecurlybraces.Withinasetthereare:-"\ast \ast \ast Elements\ast \ast "-definedasamathematicalobjectwithinagivenset:$$

\text{if} \ x \in \ \text{the object} \ x \ \text{is an element of the set} \ A

- "**Sub-sets** ($\subset$)" - All $\in$ within a set is also contained in another set:

\text{B is a subset of A }

- **Union ($\cup$)** - Combination of sets

B \cup C = { x |x\in B \ or \ x \in \ C }

= 1,2,3,4,5,6

- **Intersection** ($\cap$) - The similar numbers within a set

B \cap C = { x |x\in B \ or \ x \in \ C }

= \varnothing

- **Difference** ($\setminus$) - Different numbers within a set.

B \setminus C = { x |x\in B \ or \ x \notin \ C }

= 1,3,5