Sets and Logic — Which correspondences are true?

The union corresponds to OR, the intersection to AND, the complement to the NOT logical operation.

Connection Between Sets and Logic

Set operations and logical operations are closely connected. Operations on sets show an analogy with the basic operations of propositional logic, so logic and set theory are often studied together.

Set Operations and Logical Operations

Union (A ∪ B) ↔ OR (p ∨ q)
Intersection (A ∩ B) ↔ AND (p ∧ q)
Complement (A') ↔ NOT (¬p)

This correspondence allows the use of logical tools when examining sets, and vice versa: illustrating logical problems with sets.

Truth Tables

The truth table shows the exact behavior of logical operations. For two statements, there are four possible truth value combinations, on the basis of which the functioning of AND, OR, and NOT can be tabulated.

Everyday Examples

"Tomorrow the sun will shine AND it will be warm." → True only if both conditions are true.
"Tomorrow the sun will shine OR it will rain." → True even if at least one condition is met.
"NOT raining." → True if it really isn't raining.

Summary

The connection between set operations and logical operations helps to better understand both. Sets visually illustrate logical relationships, while logic provides a precise description of set operations.

Practice Exercise

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