3. All that is, ever was, or ever will be is contained within the Universe. All that is, ever was, or ever will be is contained within the Universe. For our purposes today the Universe exists only within the borders of this screen. For our purposes today the Universe exists only within the borders of this screen.

4. Everything contained within this screen creates a set of things. Everything contained within this screen creates a set of things. The set of all things is called - The set of all things is called -

5. Everything contained with this screen creates a set of things. Everything contained with this screen creates a set of things. The set of all things is called - The set of all things is called -

6. George Boole, 1815 – 1864. In 1854 he developed the algebra of logic that now bears his name, Boolean Logic, and published it in a book entitled, An investigation into the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities. All computers today use Boolean algebra to perform tasks that require logical analysis – even handheld calculators. Searching computer databases for information often Requires the use of Boolean Logic, too. There are three main logical operations in Boolean Logic – AND OR NOT These are the Boolean Operators.

7. The ancient Chinese symbol for the forces of good and evil, Yin and Yang, is also a way of depicting the Universe in terms of sets. John Venn, 1834 – 1923. In 1881 Venn published Symbolic Logic, his most important work, which laid out modern Set Theory. Venn extended Boolean Logic and is best known for inventing a way of showing sets and their logical relationships called Venn Diagrams. But he was not the first to think of describing the Universe in terms of sets.

9. The Universal Set The Universal Set is a boundless imaginary container that can hold an infinite number of other imaginary containers - SETS. is a boundless imaginary container that can hold an infinite number of other imaginary containers - SETS.

10. A circle is used to define the bounds of a new Set. A circle is used to define the bounds of a new Set.

11. A label defines what is in the new Set. A circle is used to define the bounds of a new Set. A circle is used to define the bounds of a new Set. A label defines what is in the new Set.

12. Anything that IS COMET cannot exist outside the bounds of this set. Anything that IS COMET cannot exist outside the bounds of this set. Anything that IS NOT COMET cannot exist inside the bounds of this set. Anything that IS NOT COMET cannot exist inside the bounds of this set.

13. NOT Comets NOT Comets NOT Comets NOT Comets This single set defines two mutually exclusive areas within the Universal Set – COMETS and NOT COMETS. This single set defines two mutually exclusive areas within the Universal Set – COMETS and NOT COMETS.

14. The three main logical relationships among Sets are defined by the Boolean Operators - The three main logical relationships among Sets are defined by the Boolean Operators - AND OR NOT AND OR NOT The logical relationships defined among Sets using the Boolean Operators create new Sets. The logical relationships defined among Sets using the Boolean Operators create new Sets.

15. The two Sets {Comets} and {Asteroids} overlap.

16. AND The Boolean Operator AND defines the area where the two Sets intersect. The Boolean Operator AND defines the area where the two Sets intersect.

17. AND This defines the new Set {Comets AND Asteroids}. This defines the new Set {Comets AND Asteroids}

18. AND The Set {Comets} contains only comets. The Set {Comets} contains only comets.

19. AND The Set {Asteroids} contains only asteroids. The Set {Asteroids} contains only asteroids.

20. AND The new set {Comets AND Asteroids} contains both comets and asteroids. The new set {Comets AND Asteroids} contains both comets and asteroids.

21. Sets {Nebulas} and {Novas} overlap. Sets {Nebulas} and {Novas} overlap.

22. OR Boolean Operator OR unites the two Sets into one. Boolean Operator OR unites the two Sets into one.

23. OR Set {Nebulas OR Novas} is now a unified Set. Set {Nebulas OR Novas} is now a unified Set.

25. Sets {Pulsars} and {Black Holes} overlap. Sets {Pulsars} and {Black Holes} overlap.

26. NOT Boolean Operator NOT excludes set {Black Holes}. Boolean Operator NOT excludes set {Black Holes}.

27. NOT Only the portion of Set {Pulsars} that does NOT intersect with Set {Black Holes} remains. Only the portion of Set {Pulsars} that does NOT intersect with Set {Black Holes} remains.

28. NOT This creates the new Set {Pulsars NOT Black Holes}. This creates the new Set {Pulsars NOT Black Holes}.

29. AND AND OR OR NOT NOT Finds the intersection of two sets. Narrows and focuses. Requires co-occurrence. Unifies two or more sets into one. Broadens, includes, and expands. Creates a general concept. Removes one set from another. Narrows and excludes. Eliminates undesired elements.

30. Generally, the order of execution of the Boolean Operators is as follows: Generally, the order of execution of the Boolean Operators is as follows: AND OR AND OR NOT NOT It is important to remember this order of precedence when creating and diagramming a Boolean Expression. It is important to remember this order of precedence when creating and diagramming a Boolean Expression.

31. Sun Moon AND

32. Sun Moon OR

33. Sun Moon NOT

34. AND NOT Sun Stars Moon

35. AND OR Sun Stars Moon

36. OR AND (Sun Stars) Moon

37. OR OR Sun Stars Moon