Practice for logical
operators
Boolean search statements
and
Venn diagrams
Tefko Saracevic, Rutgers
University
1
Exact match - Boolean
search
• You retrieve exactly what you
ask for in the query:
– all documents that have the term(s)
with logical connection(s), and
possible other restrictions (e.g. to
be in titles) as stated in the query
– exactly: nothing less, nothing more
• Based on matching following
rules of Boolean algebra, or
algebra of sets
– ‘new algebra’
– presented by circles in Venn
Tefko Saracevic,
Rutgers
diagrams
University
2
Boolean algebra & Venn
diagrams
Four basic operations:
A
1
B
2
A
3
A alone. All documents that have A.
Shade 1 & 2. E.G. apples
B
1 2 3
A AND B. Shade 2
apples AND oranges
A
B
1 2 3
A OR B. Shade 1, 2, 3
apples OR oranges
A
B
1 2 3
A NOT B. Shade 1
apples NOT oranges
Tefko Saracevic, Rutgers
University
3
Venn diagrams … cont.
Complex statements allowed e.g
A
B
2
3
1
4
5
(A OR B) AND C
Shade 4,5,6
6
7
(apples or oranges) AND
Florida
C
(A OR B) NOT C
Shade what?
(apples or oranges NOT
Florida
Tefko Saracevic, Rutgers
University
4
Directions for exercise
• Slide 7 provides a Venn diagram
with numbered sets and a number
of search statements
– for each statement shade the
appropriate set or sets
– e.g. for (A OR B) AND C the sets
are 4, 5, 6
• Slide 8 is for practice
• Slide 9 has the answers
– BUT NOTE: one of the answers is
WRONG! Which one?
Tefko Saracevic, Rutgers
University
5
Order of operations
• Rules for the order in which
operations are done effect the
answer - so follow them
• Dialog order of operation is:
1. First are done all operations that are
in parentheses, then:
2. (W), (N), (S), (L), or (F)
3. NOT
4. AND
5. OR
• e.g. for A OR B AND C, first is
done B AND C, and then A OR the
results of B AND C, thus this is the
same as A OR (B AND C)
Tefko Saracevic, Rutgers
University
6
Venn diagrams
A
B
1
2
4
5
3
6
7
C
1. A AND B
2. A OR B
3. A OR B AND C
4. (A OR B) AND C
5. A AND B NOT C
6. A AND (B NOT C)
7. (A AND B) NOT C
8. (A NOT B) AND C
9. A NOT (B AND C)
10. A NOT B AND C
11. A AND (B OR C)
12. A AND B OR C
13. A OR (B AND C)
14. A OR B OR C
15 A AND B AND C
Tefko Saracevic, Rutgers
University
7
Use for exercise & shading
A
B
2
3
1
4
5
6
7
C
Tefko Saracevic, Rutgers
University
8
Venn diagrams: solutions
p.s. one of them is wrong!
A
B
1
2
4
5
3
6
7
C
1. A AND B
2,5
2. A OR B
1,2,3,4,5,6
3. A OR B AND C
1,2,4,5,6
4. (A OR B) AND C
4,5,6
5. A AND B NOT C
2
6. A AND (B NOT C)
2
7. (A AND B) NOT C
2
8. (A NOT B) AND C
4
9. A NOT (B AND C)
6
10. A NOT B AND C
4
11. A AND (B OR C)
2,4,5
12. A AND B OR C
2,4,5,6,7
13. A OR (B AND C)
1,2,4,5,6
14. A OR B OR C
1,2,3,4,5,6,7
15 A AND B AND C
5
Tefko Saracevic, Rutgers
University
9