Operation of set- union Intersection and Difference

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ScanSolve AI Tutor · Accepted Answer

Set operations define ways to combine or compare sets. The three fundamental operations are:

Union ( $\cup$ )
The union of two sets, A and B, denoted as $A \cup B$ , is the set containing all elements that are in A, or in B, or in both.
- Example: If $A = \{1, 2, 3\}$ and $B = \{3, 4, 5\}$ , then $A \cup B = \{1, 2, 3, 4, 5\}$ .
Intersection ( $\cap$ )
The intersection of two sets, A and B, denoted as $A \cap B$ , is the set containing all elements that are common to both A and B.
- Example: If $A = \{1, 2, 3\}$ and $B = \{3, 4, 5\}$ , then $A \cap B = \{3\}$ .
Difference ( $-$ or $\setminus$ )
The difference of two sets, A and B, denoted as $A - B$ or $A \setminus B$ , is the set containing all elements that are in A but not in B.
- Example: If $A = \{1, 2, 3\}$ and $B = \{3, 4, 5\}$ , then $A - B = \{1, 2\}$ .
- Note that $B - A = \{4, 5\}$ in this example, showing that set difference is not commutative.

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