If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A union B, A intersection B, and A minus B.

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> [!TLDR]
> The key idea is to apply the standard set operations — union (all elements from both sets), intersection (common elements), and difference (elements in A not in B). For $A = \{1,2,3,4\}$ and $B = \{3,4,5,6\}$, we get $A \cup B = \{1,2,3,4,5,6\}$, $A \cap B = \{3,4\}$, and $A - B = \{1,2\}$.

This problem is a straightforward exercise in the three fundamental set operations. Understanding these operations is essential because they form the building blocks for everything from probability to database queries. Let's break each one down.

**1. Union ($A \cup B$)** — The union of two sets is the set of all elements that belong to *at least one* of the sets. Think of it as "combining" the two collections without repeating any element.

We list every element from $A$ and $B$:
- From $A$: 1, 2, 3, 4
- From $B$: 3, 4, 5, 6

Now, remove duplicates (3 and 4 appear in both). The combined collection is $\{1, 2, 3, 4, 5, 6\}$.

> [!TIP]
> A quick way to find the union: write down all elements of the first set, then add any element from the second set that isn't already listed. This avoids accidental omission.

**2. Intersection ($A \cap B$)** — The intersection is the set of elements that are *common* to both sets. Only the elements that appear in both $A$ and $B$ qualify.

Scan both sets:
- 1 is in $A$ but not in $B$ → no.
- 2 is in $A$ but not in $B$ → no.
- 3 is in both $A$ and $B$ → yes.
- 4 is in both $A$ and $B$ → yes.
- 5 and 6 are only in $B$ → no.

So the intersection is $\{3, 4\}$. …

Operation	What it asks	Bucket contains
Union ( $A \cup B$ )	In either?	Everything from $A$ or $B$ (or both)
Intersection ( $A \cap B$ )	In both?	Only the overlap
Difference ( $A \setminus B$ )	In $A$ but not $B$ ?	Just the part of $A$ that doesn't touch $B$
Complement ( $A^c$ )	Not in $A$ ?	Everything outside $A$ (inside $U$ )
Symmetric Difference ( $A \triangle B$ )	In exactly one?	The two crescent-shaped parts, excluding the overlap

Q.If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A union B, A intersection B, and A minus B.

Concept understanding — Set Operations

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Q.If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A union B, A intersection B, and A minus B.

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